1) you could hustle and do it in a few weeks with good weather
but i'd do a few months and make it somewhat enjoyable. you can leave around october with the baja-haha if you like. might make for some good company especially if you're not familiar with the area.
2) leaving in late october would be good. most of the nasty stuff is june-november. i'm not sure about the other side of the country though (gulf of mexico).
3) you should be able to get something fine for that amount of money
. maybe shoot for ~40k and spend the rest getting it set up the way you want. save your money
the best you can and get things as you need them. a lot of people buy stuff they think they'll need only to find later that they didn't, or they need something else more and don't have the funds.