Ok, my tone was probably poor too.. Understand at 21, I SHOULD have thought like you! I'd have had a blast! but I digress, and I had NO cash at all.
Alright, skills you got on repairs (welder = tinkerer to me)... Mech E! Good gonzo's you can fix things for sure (I went the EE route, my buddies who couldn't hack it went the Mech E route - not a knock, just an engineering joke).
Ok, live aboard for next summer is what you are after... THAT explains why they steered you towards a 25. A catalina 22 swing keel, will be probably the "average" of everything you are looking for, the "jack of all trades" if you will... but I honestly don't think it'd be a great fit, more of that "master of none" part of that.
As others have said, if your intent is to live aboard (even for the 4-6 months)... make sure the Marina will allow you to do so. The 22 footer would be the 2 man tent. a 25 footer would be more like a 6 man tent, with an enclosed latrine.
Looking at the lake, and checking around to various marina's on that lake, looks like it is NOT uncommon for a 27 footer there. I know it must be deep as most the finger lakes are. So size is only a problem for towing, not for sailing, you likely could go as big as 32 feet as long as you could get it out of the water come fall (since the lake freezes).
OK, so learning... well, this is the next thing, I am going to go against the grain here, and say it is MUCH easier to sail a larger boat (to a point)... a 25 or 27 foot sailboat, is going to be infinitely more forgiving than a 16-20 foot boat, and infinitely still more forgiving than a sailing/racing dinghy. That being said, the smaller boats teach you faster (as it is literally sink or swim), so don't count that idea out either, nothing wrong with an apartment and a Lido 14!
OK... Here is a thought for you, since you live in VA, and school in NY... and your taco isn't gonna get you pulling a comfortable live-aboard type... (Remember a Lido 14 could be towed by a VW Bug).
TAKE WHAT I SAY HERE WITH A GRAIN OF SALT, IT WOULD BE WHAT I'D do at your age with $4000 burning a hole in my pocket. It isn't right, it likely isn't smart, but it'd be a damned fun thing to do, and something you can tell your grandkids about when they grow up.
Buy a 27 footer, that has a trailer, or at least a 26 footer, better said a 25 or bigger boat with a trailer (that is sailable now might need work, but sailable - there are a lot). Get a boat with an enclosed head! Put it in a marina (remember marina fees here, as that'll likely run you about $1500 for the season). When it comes time to go home with the boat, RENT A UHAUL pickup to tow it home (or van)... it'll have plenty of towing capabilities, and it'll get it home for ya. Worry about putting it back in the water when you get to that the following spring.
OK, at 25 feet you are on the edge of FUN of lifting a mast, but 3 good college buddies, and you are set.
Live on the darned thing. Make sure to pick a nice marina, with showers, and laundry, and a clubhouse. Be the young punk kid with good taste that all the old salts wish were you (never be scummy or obnoxious drunk kid in the clubhouse). Crew for ANY of these old salts, offer help when they launch their boats... HELL invite the old salts out on your BOAT tell them you'd like them to skipper for you! Pickup crewing jobs on race crews while you are there (look for BEER can races run on weekends all summer). Enter them yourself if you can scare up some guys to crew for you.
Finally, enjoy your stay there. Help the dockmaster (because he is putting up with your keester being there all summer). Offer to do odd jobs for him... Hell make sure to offer him a beer or 2 when he heads your way (his can be a tough job at times, and he is an indispensable friend to have).
You'll be CAMPING full time for sure, especially on the smaller side of these boats, but a summer is definitely doable, and For GOD's sake boy, report back to us!
Websites that can help you find boats (sailboatlistings, sailing texas) likely won't help you find one on your lake (they can but mostly they give regions), try craigslist, and NOW is the best time to buy (maybe buy one on the hard in someone's yard, offer them X more dollars to allow you to keep it in their yard until spring, then rent that UHAUL and put it in the water in spring (get those college buddies to help you as a 25+ footer will be a pig to launch).
OH, here's one better, you want help in spring? I'll freaking drive up to help (you're about 4-5 hours away). I take my payments in beer! Hell I'll even help you shake the new to you boat down if you'd like. Just PM me when and where!
I am gonna say what a lot of these guys won't. You are young, we are jealous, go have fun! Just do it safely, respectfully, learn what you can, and enjoy it!
That is just my $0.02 from a 40 year old sailor who really is JUST now starting to enjoy sailing for sailing's sake again. I haven't been out of sailing, just not been sailing with the right attitude. Sounds like you got the right attitude, now go do it!
PM: me if you want to bounce ideas of boats you are looking at. Finally you'll likely be getting something bigger than I have now (your lake is larger)... I have a Dodge 2500, RAM and can tow a really large sailboat if need be, I'll again do it for beer and gas money.
OK GUYS FLAME ME AS AN ENABLER! hehehe. My wife is gonna know I am off my rocker now.