Re: New to the sport
A Catalina would be a good move, even if only on the resale front. And I'd expect you'll find a nice C27 for WAY less than $30K, maybe even $10K, and you should be able to find a C30 in your price range too - along with a number of other boats in that size range and from probably the 80s...
Lake sailing, I presume, for starters? Marina based? or as mentioned already, trailerable?
Your plan sounds do-able, best of luck.
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)