Hot Vibrato has summed it up very nicely for you regarding carved top and laminate guitars. If you want to go the electric way then a laminated guitar will be good from the feedback point of view, but they are not so clever when played acoustically. Obviously you can play them acoustically but they lack the tone and volume of a carved top instrument.
The Gibson ES175 is the achetypical laminated electric jazz box, but even second hand is out of your range of prices. Eastman may come to your rescue here with their AR371CE model which is a single pickup variant of a 175. The AR372 has two pickups and perhaps second-hand would fall into budget for you. I think a carved top guitar, even from Eastman, will be outside what you want to pay.
Incidentally, I have an Eastman AR371CE and find it great for me, a beginner at jazz guitar.
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