What To Collect...

My first completed set was Franklin half dollars. Not classic coins, but possible to complete with circulated coins in the junk silver trays at coin shops.

type of classic coin to collect
IHC or Mercury dimes would be my suggestion.
John1

If you aren't afraid that your "collection" would have several empty holes for multi-hundred-dollar coins, then Mercury dimes, or perhaps wheat cents (but I don't think they count as "classic").
I agree that Buffalo nickels will probably have the lowest total cost (perhaps less even than Franklin halves, depending on what grade you're looking for).

On a completely whimsical suggestion: Braided Hair large cents. It's a beautiful design, and a nice reasonably challenging set with some uncommon dates but no $200+ key.

Not "classic," but scratches the itch of building a decent sized set, on the cheap--state and ATB Washington quarters (1999-date). There are lots of them--two for each state (P,D) and the series continues after that with territory and ATB Quarters. This set still can be built from circulation and gives ya sumpin' to look for daily. Or you can opt for much choicer specimens (some slabbed) that are available to purchase.

You might look back on such a set many years from now and be glad you put a set together when available from circulation (like many of us fossils wish we had done with coins in circulation when we were 17-year-old kids. {grin})

edit: oh, and I like the type set idea too. And consider foreign (British, Canadian, etc.)--cheaper, less demand--like Canadian large cents (1858-1920).

The large cent (classic, coronet, braided hair) idea is actually a really good choice. Not only are all the coins well over 100 years old they are relatively "cheap" in acceptable grades. The coins have also been studied to death for varieties and there is a lot of information available on these type/varieties. The best part would be it's not the "typical starter" collection.

I'd ask what your budget / coin might be and if you are OK with 20th Century or had you heart set on 19th century. Also what grades of coins are you happy with. For 19th Century, large cents and bust dimes is where I started out. Cost for most coins if you are generally savvy and will be OK with G/VG graded items is $10-30 per coin and over the course of a few short years a substantial date set can be established. 2Cent and 3Cent Nickels would fall into this category too. For Morgans in circulated condition, a lot of them are around $30ish. If this is beyond your means with upcoming school expenses, Indian Heads, V nickels, and Barber dimes are sets that covered the turn of the century could be your best bets. Otherwise, the focus will be on 20th century types.

The Peace dollar is a nice coin to collect since there are not that many of them, and only a few are more than a few hundred dollars. If you collect the Peace dollar you have a big silver coin that has been overlooked by silver dollar collectors who focus on the Morgans. You could spend $500,000 collecting Morgans, but you could also collect the 40 most common ones in MS condition for less than $100 a piece. Mercury dimes and Buffalo nickels do make sense for beginners with limited budgets. If as a 17 year old you could collect early 20th century coins and hold them I bet you could cash out on day for big bucks. Some of the most beautiful coins were minted in 20th century. I would collect silver and gold coins.