$2000-$6000 is probably not going to get you much of an RV. 6K maybe. 2K doubt it. Pretty much all average level RV's are slapped together by the same cheap labor. Good thing you have until Feb to look around. You can probably find a deal if you look hard enough, but you need to be pretty good at fixing things because likely whatever you find will have issues. If you've not owned an RV before, bone up on what to look for when checking out used ones, especially in that price range. I don't know that Jayco's are any more 'cheaply made' than any other brand. And, at your price point, the model makes no difference. As Tom/Barb says - it's all in how it was taken care of.
Some RV parks have age limits on RV's. The ones in the $300-500 price range may not. At your price point, you're looking at an older RV. Just about every place, if you are a monthly renter, you have to factor in utilities as well.
Are you looking at a TT or 5er, or self contained? Do you have a tow vehicle? Are you prepared to live full time in about 200 SQ FT or less? How do you feel about having neighbors within about 5 feet or so of you or so? Wherever you go, you will need to have a full hookup site, unless you want to haul to a dump station every couple three or four days (depending on tank size).
Not saying you can't do it, but you need to think it through.
Mike
