Best Boat for Mixed Bay and Offshore

[Slidellkid]

I want to be able to go offshore and catch Cobia, snapper, kings. I have been thinking of a 22-24 foot bay boat and I believe I could do just fine with it, but could I do better if I got something like a 19 Cape Horn or 20 Sea Hunt or 19 Pioneer as a do all boat. How much of a handicap, if any, is a regular center console in Big Lake or the marsh versus a bay boat, assuming I can put a trolling motor up front. Many of the 19 and 20 center consoles have the smaller or shallower draft as the larger bay boats.

My thinking was that a 24 foot bay boat is very expensive and I can get a 19 or 20 foot center console (barley used) for 16-20k.