ASert, getting rid of the squeeze around your crotch takes a couple of dives to get used to but you can get there. I'd definitely recommend a dry suit, as one skinny guy to another.
I get cold easily. I have I think 8 or 9 wetsuits ranging from a 2.5mm spring suit (long sleeves, short legs) to a 7 mm step in jacket. When I'm diving wet, I layer as necessary. A hooded vest works wonders for adding warmth without a lot of extra buoyancy to worry about. For your area I'd definitely say at least a good 5mm but more likely a 7mm for wet and a dry suit of some kind.
Look for used dry suits too, as you can often get great deals. I bought my TLS350 (DUI) for $200 on Craigslist. After half a dozen dives I spent another $400 putting new silicone neck and wrist "zip seals" (my skinny wrists allowed too much leakage with the latex seals) and I'm still more than $2000 less than retail for the suit. Likely you won't find a deal quite as good as that but $500 for a used dry suit is fairly common to see.
EDIT: To give some concept of my exposure protection, I'm 6'1, 170 and have between 2-5% body fat, depending upon my exercise regime of the day. In the freshwater quarry here, when diving wet, I wear ~14mm on my core. A 4/3 full suit or a 5mm full suit, with a 5/3 hooded vest (3 on the chest), with a 7mm step in jacket over top of all that. That keeps me toasty in temps down to about 50 degrees for a couple of short dives. It keeps me tolerably warm down to about 45 for a couple of shorter dives. It keeps me almost warm lower than 45 for 1 short dive and just plain cold for a second dive.
I wear at least a 4/3 full suit in anything below 80 degrees. In warmer water than that, I start going down to a 3mm or the shorty. I tried the 2.5mm spring suit with the hooded vest at Rainbow river in FL but found I was too cold. The water there is, I believe, 76* year round.