Coins To Look Out For In UK

Without hopefully sounding negative its probably anything you like the look of.
The UK has gone decimal beserk and the chance of you finding anything scarce or unusual in your change I feel would be slim.
I live here and never see or find anything ,people often go to banks and draw out large amounts to sort through and feel the change from a purchase such as the odd £2 ,50p or 10p would just give you normal circulation change.
Any £2 ,50p or 10p maybe worth you looking for different types and the others there are millions of so maybe just get one of each of the £1,20p,5p,2p & 1p if you can find any that look nice and uncirculated.
The Banknotes are the same and maybe just get one of each of the polymer £10 & £5 which you will again find easily and are often in good condition due to them now being made to last longer.
Have a good time and atleast you are coming over to some nice weather.

Very much what pwa1967 said.

The chance of you finding anything in your change is almost nil. But for that gazillion to one chance, here are some suggestions -

£2

2002 commonwealth games
4 almost identical designs,

2008 centenary of 4th olympiad

2013 150th anniversary of London underground, 2 designs

2015 ww1 Royal Navy warship, along with any other ww1 design from surrounding years

2015 Britannia and later


£1 - nothing of note

50p -
2009 kew gardens [ looks up and sees elephant flying up into clouded sunset ]
2011 olympics, 29 designs for 2012 olympic games
2014 commonwealth games
2015 Battle of Britain
2016 team GB olympics
2017 Isaac Newton

Of smaller coins, only the alphabet 10p's, [ sees flying pig chasing elephant ].

There are some scams to avoid -

So-called upside down edge writing on £2. Either way up is equally likely.

1997 necklace design on £2. The design of the obverse changed in 1998, where the queen's effigy no longer has a necklace. Only (!) 13.7 million of the 1997 design were issued. It is the only year of that design but not particularly rare.

Lots of 50p kew gardens fakes.

Bimetallic coins where the queen's head is on the wrong side. This is impossible to occur during manufacture, somebody has done it post mint.

Edge inscriptions where part of the letter is missing, eg 'PEMEMBER' instead of 'REMEMBER'. These do occur but are not worth much over the basic coin.

Happy hunting.

Furthering to Anaximander's post:

The 2008 Olympic Games Handover, 2011 King James Bible and 2012 Olympic Games Handover £2 coins all have mintages under a million. The 2011 Mary Rose is pretty scarce, too.

For 50ps the 2017 Shield is rather scarce, too.

I guess also the undated 20p, though you've really much more chance of being struck by lightning I expect.

For the banknotes the only real things to look for might be any cool serial numbers.

Another nonsense idea to avoid:
The "AA/AK47 £5 notes/JA £10 notes are worth a gazillion pounds because they're super rare" etc frenzy.

Really though, keep what you like.