US East Coast? I did an awful lot of research on that very question, and my conclusion pointed to Mid 1960s to Late 1970 vintage Pearsons. If you want truly venerable, a Pearson Triton.
The Pearson 33, Pearson 32, and Pearson 10M are all at the top end of your size range, strongly built hulls with solid deck to hull joints, generally fast-ish and sea kindly, and generic enough in the interior that you won't feel bad about cutting it up.
And there's a wealth boats available the 20-30 foot range, too. Each has it's strengths and weaknesses for various types of sailing, so read up on any that catch your eye.
Any conversion is going to make a compromise of some sort regarding plunking a mast in the not-quite-optimal interior location. But start with a well designed hull, properly built, and a deck that ain't rotted.
I'm not an old man but I'm going to sound like one here: when it comes to production boats, they don't make them like they used to.
Also - you might not find your $100 fixit boat on Yachtworld. Most of them are close to sail-able right away, or they wouldn't be saleable enough to get a broker. Make a habit of driving around the local marinas and looking at the boats on the hard with grass growing under them. If you find a Pearson tucked in the back corner with the washboards all grey and the hull dull and streaked - that may just be your girl. Ask the yard manager about her.
But just to make my last paragraph have less authority, there are gals like this on Yachtworld:
http://www.yachtworld.com/boats/1977/Pearson-26-SLOOP-2767469/pine-beach/NJ/United-States#.WW4nzIQrJaQ
Or, oh boy! An Alberg designed Pearson Ariel just waiting to get reworked into a junk. This is one tough boat. http://www.yachtworld.com/boats/1977/Pearson-26-SLOOP-2767469/pine-beach/NJ/United-States#.WW4nzIQrJaQ