Hello and 
I'd recommend you get a catalog of British coins. Something like Seaby's Coins of England or Coin Year Book should be adequate.
Type collectors would probably consider the following 'type sets' for the 19th and 20th centuries:
George III coinage reform 1806 - 1820
Copper farthing, halfpenny and penny
Silver sixpence, shilling, halfcrown and crown
Gold half-sovereign and sovereign
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George IV first porttrait 1820 - 1826
Copper farthing
Silver sixpence, shilling, halfcrown and crown
Gold half-sovereign, sovereign and £2
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George IV second porttrait 1825 - 1830
Copper farthing, halfpenny and penny
Silver sixpence, shilling and halfcrown
Gold half-sovereign and sovereign
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
William IV 1831 - 1837
Copper farthing, halfpenny and penny
Silver groat, sixpence, shilling and halfcrown
Gold half-sovereign and sovereign
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Victoria Young Head (1838 - 1887)
Copper half-farthing, farthing, halfpenny and penny (up to 1860)
Silver threepence, groat, sixpence, shilling, halfcrown and crown
Gold half-sovereign and sovereign
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Victoria 'bun head' - bronze farthing, halfpenny and penny only 1860-94
Victoria 'Gothic head' - silver florin 1851-87 and crown 1847-53 only
Victoria Jubilee Head 1887-93
Silver threepence, groat, sixpence, shilling, florin, halfcrown, double-florin and crown
Gold half-sovereign, sovereign, £2 and £5
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Victoria Veiled Head 1893 - 1901
Bronze farthing, halfpenny and penny
Silver threepence, sixpence, shilling, florin, halfcrown and crown
Gold half-sovereign, sovereign, £2 and £5
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Edward VII 1902 - 1910
Bronze farthing, halfpenny and penny
Silver threepence, sixpence, shilling, florin, halfcrown and crown
Gold half-sovereign, sovereign, £2 and £5
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George V first issue 1911 - 1927
Bronze farthing, halfpenny and penny
Silver threepence, sixpence, shilling, florin and halfcrown (92.5% until 1920)
Silver threepence, sixpence, shilling, florin and halfcrown (50% from 1920)
Gold half-sovereign, sovereign, £2 and £5
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George V second issue 1927 - 1936 (modified head, new reverses)
Bronze farthing, halfpenny and penny
50% Silver threepence, sixpence, shilling, florin, halfcrown and crown
Gold sovereign (Commonwealth mints only)
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George VI first issue 1937 - 1948 with IND:IMP on obverse
Bronze farthing, halfpenny and penny
Nickel-brass threepence
50% Silver threepence, sixpence, English and Scottish shillings, florin, halfcrown (all issued 1937-46); crown (1937 only)
Cupro-nickel sixpence, English and Scottish shillings, florin, halfcrown (all issued 1947 and 1948)
Gold half sovereign, sovereign, £2 and £5 (1937 proof sets only)
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George VI second issue 1949 - 1952 without IND:IMP on obverse
Bronze farthing, halfpenny and penny
Nickel-brass threepence
Cupro-nickel sixpence, English and Scottish shillings, florin, halfcrown (sixpence has new reverse design); Crown (1951 only)
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Elizabeth II first issue 1953 with BRITT: OMN on obverse
Bronze farthing, halfpenny and penny
Nickel-brass threepence
Cupro-nickel sixpence, English and Scottish shillings, florin, halfcrown, crown
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Elizabeth II second issue 1954 - 1967 without BRITT: OMN on obverse
Bronze farthing (1954-56 only), halfpenny and penny (1961-67 only)
Nickel-brass threepence
Cupro-nickel sixpence, English and Scottish shillings, florin, halfcrown; crown (1960 only); 1965 crown commemorating Winston Churchill.
Gold sovereign (1957 - 67, struck for collectors and bank reserve)
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d) issued up to 2022 with same design.
Elizabeth II first decimal issue 1971 - 1981. Machin portrait, coins have 'NEW'
Bronze halfpenny, penny and twopence
Cupro-nickel five pence, ten pence and fifty pence (first issued 1968/9)
Elizabeth II second decimal issue 1982 - 1984. Machin portrait, coins don't have 'NEW'
Bronze halfpenny, penny and twopence
Cupro-nickel five pence, ten pence, twenty pence and fifty pence
Nickel-brass £1 (introduced 1983, reverse changes each year)
Elizabeth II third decimal issue 1985 - 1997. Maklouf portrait
Bronze penny and twopence (copper-clad steel from 1992)
Cupro-nickel five pence, ten pence, twenty pence and fifty pence
Nickel-brass £1 (reverse changes each year)
(Lots of commemorative coins start appearing now)
Elizabeth II fourth decimal issue 1998 - 2008. Rank-Broadley portrait
Copper-clad steel penny and twopence
Cupro-nickel five pence, ten pence, twenty pence and fifty pence
Nickel-brass £1 (reverse changes each year)
(Lots of commemorative coins)
You could include coins issued for certain British colonies such as the quarter-farthing, third-farthing and one-and-a-half pence, whiich are often listed in British catalogs.
I don't know of any albums made for British type sets. Years ago you could get Sandhill Cases to house sets of coins, and a company called Bri-Lining made albums which held sets in card inserts like this:

I'd recommend you get a catalog of British coins. Something like Seaby's Coins of England or Coin Year Book should be adequate.
Type collectors would probably consider the following 'type sets' for the 19th and 20th centuries:
George III coinage reform 1806 - 1820
Copper farthing, halfpenny and penny
Silver sixpence, shilling, halfcrown and crown
Gold half-sovereign and sovereign
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George IV first porttrait 1820 - 1826
Copper farthing
Silver sixpence, shilling, halfcrown and crown
Gold half-sovereign, sovereign and £2
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George IV second porttrait 1825 - 1830
Copper farthing, halfpenny and penny
Silver sixpence, shilling and halfcrown
Gold half-sovereign and sovereign
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
William IV 1831 - 1837
Copper farthing, halfpenny and penny
Silver groat, sixpence, shilling and halfcrown
Gold half-sovereign and sovereign
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Victoria Young Head (1838 - 1887)
Copper half-farthing, farthing, halfpenny and penny (up to 1860)
Silver threepence, groat, sixpence, shilling, halfcrown and crown
Gold half-sovereign and sovereign
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Victoria 'bun head' - bronze farthing, halfpenny and penny only 1860-94
Victoria 'Gothic head' - silver florin 1851-87 and crown 1847-53 only
Victoria Jubilee Head 1887-93
Silver threepence, groat, sixpence, shilling, florin, halfcrown, double-florin and crown
Gold half-sovereign, sovereign, £2 and £5
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Victoria Veiled Head 1893 - 1901
Bronze farthing, halfpenny and penny
Silver threepence, sixpence, shilling, florin, halfcrown and crown
Gold half-sovereign, sovereign, £2 and £5
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Edward VII 1902 - 1910
Bronze farthing, halfpenny and penny
Silver threepence, sixpence, shilling, florin, halfcrown and crown
Gold half-sovereign, sovereign, £2 and £5
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George V first issue 1911 - 1927
Bronze farthing, halfpenny and penny
Silver threepence, sixpence, shilling, florin and halfcrown (92.5% until 1920)
Silver threepence, sixpence, shilling, florin and halfcrown (50% from 1920)
Gold half-sovereign, sovereign, £2 and £5
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George V second issue 1927 - 1936 (modified head, new reverses)
Bronze farthing, halfpenny and penny
50% Silver threepence, sixpence, shilling, florin, halfcrown and crown
Gold sovereign (Commonwealth mints only)
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George VI first issue 1937 - 1948 with IND:IMP on obverse
Bronze farthing, halfpenny and penny
Nickel-brass threepence
50% Silver threepence, sixpence, English and Scottish shillings, florin, halfcrown (all issued 1937-46); crown (1937 only)
Cupro-nickel sixpence, English and Scottish shillings, florin, halfcrown (all issued 1947 and 1948)
Gold half sovereign, sovereign, £2 and £5 (1937 proof sets only)
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
George VI second issue 1949 - 1952 without IND:IMP on obverse
Bronze farthing, halfpenny and penny
Nickel-brass threepence
Cupro-nickel sixpence, English and Scottish shillings, florin, halfcrown (sixpence has new reverse design); Crown (1951 only)
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Elizabeth II first issue 1953 with BRITT: OMN on obverse
Bronze farthing, halfpenny and penny
Nickel-brass threepence
Cupro-nickel sixpence, English and Scottish shillings, florin, halfcrown, crown
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d)
Elizabeth II second issue 1954 - 1967 without BRITT: OMN on obverse
Bronze farthing (1954-56 only), halfpenny and penny (1961-67 only)
Nickel-brass threepence
Cupro-nickel sixpence, English and Scottish shillings, florin, halfcrown; crown (1960 only); 1965 crown commemorating Winston Churchill.
Gold sovereign (1957 - 67, struck for collectors and bank reserve)
Optional: Maundy Set (small silver 1d, 2d, 3d and 4d) issued up to 2022 with same design.
Elizabeth II first decimal issue 1971 - 1981. Machin portrait, coins have 'NEW'
Bronze halfpenny, penny and twopence
Cupro-nickel five pence, ten pence and fifty pence (first issued 1968/9)
Elizabeth II second decimal issue 1982 - 1984. Machin portrait, coins don't have 'NEW'
Bronze halfpenny, penny and twopence
Cupro-nickel five pence, ten pence, twenty pence and fifty pence
Nickel-brass £1 (introduced 1983, reverse changes each year)
Elizabeth II third decimal issue 1985 - 1997. Maklouf portrait
Bronze penny and twopence (copper-clad steel from 1992)
Cupro-nickel five pence, ten pence, twenty pence and fifty pence
Nickel-brass £1 (reverse changes each year)
(Lots of commemorative coins start appearing now)
Elizabeth II fourth decimal issue 1998 - 2008. Rank-Broadley portrait
Copper-clad steel penny and twopence
Cupro-nickel five pence, ten pence, twenty pence and fifty pence
Nickel-brass £1 (reverse changes each year)
(Lots of commemorative coins)
You could include coins issued for certain British colonies such as the quarter-farthing, third-farthing and one-and-a-half pence, whiich are often listed in British catalogs.
I don't know of any albums made for British type sets. Years ago you could get Sandhill Cases to house sets of coins, and a company called Bri-Lining made albums which held sets in card inserts like this:






















