Your budget is not realistic. A SAFE boat that can sail 6 comfortably cannot be had for $20K. I also wonder if you understand how much it costs to maintain a boat that is comfortable for 6. Figure between 5k and 10K annually - not just the first year when you are upgrading.
For your first boat, I think you would do well to buy something like a CS22/Tanzer22/Catalina 22 and sail it for a couple of years. Learn what is involved in boat ownership and how to sail properly. Then move up.
Failing that, look for a C&C 27 or a CS27, perhaps an Alberg 30, Bayfield 29. You should be able to find a fair specimen under 20K.
Be advised though, that is costs more to bring a oat back up to Bristol condition than it does to buy one that has already been updated. When you look at the boat sales sites on the internet and you see 30 foot boats averaging 30 to 50K realise that that's what they cost. You can spend it up front or you can spend it along the way, but you will spend it.
Good Luck !