My experience is bareboating, If you stay away from tourist area shopping and sail off the beaten path it can be done.
For preparation factor in a good battery bank, solar panels and wind genny (3-4k if you do the work yourself) so you can use the diesel for only motoring the boat to get somewhere. Small water makers can be had for under 2k, and might be priceless; enough solar panel output and you can make 'free' water enough for everyone.
My refridge runs on propane which is cheap just about everywhere but still runs 20 bucks for 3 weeks of ice and cold food (Dometric brand, 4cu ft).
Read up a lot from the folks like the Pardley's on how to live and sail on the cheap (tarps for rain water etc..).
It can be done. I've read books on guys living on 22 ft catalina's living off 200 a month. It can be done. We ALL hope it can be done because that's what most of us are planning
My Navy retirement check is a bit larger than your budget, but I'll add in a sizable quantity of rum and coke to my expenses. How we hope it can be done
You'll have to extend your range or risk hurricane season sitting in the center of the dartboard tho. That's where careful planning and weather window choices can get you through on a Catalina 34. I'd look older and stouter if the option is still open.