your location says midcoast maine, which is also where i fall. problem is, midcoast covers some decent area. i'm about half way between rockland and augusta, so i'm on the border of central and midcoast, but i have the same problem with a good distance to a welding shop. advantage gases / valley and maineoxy have the most loctions, but there is also lynox (outskirts of bangor) and there are some independent shops too - regulator service (augusta).
in looking for instruction, mcst in rockland usually has classes for stick, mig, and tig welding in the evenings. they aren't cheap - probably $200-$300 for a 10~ish week class. if they aren't close then there may be another school that offers them too.
i agree that tig is a great process, though it's the one i use the least, and ultimately the one that i am the least proficient in, since i get so little practice with it. my favorite thing about it is that i have much more control over how much filler metal i add, particularly compared to using wire feed. though i must say that it is my belief that limiting that to your primary / only welding choice for exhaust or body work is not the right choice. unless you are doing restorations on $100k vehicles, i think that using tig for body work and exhaust work is like putting lipstick on a pig. sure, it will work fine, and you will get good results, but it's a lot more tedious process for something that will be hidden under the vehicle, or sanded and covered with filler and paint.
as others have said, the $1k mark is going to be a hard one to hit - even worse where you live. there aren't a lot of pieces of machinery sold used in this state, and many of the ones that are listed are pretty old and used up. my guess is that you will have more luck going to a new import to meet your wants before finding a used domestic unit in your price range. i paid either $800 or $900 (can't remember anymore) used for my miller econotig setup which will do stick and tig on all metals, though it is a very rudimentary machine with virtually no fine tuning control, but the thing that many forget when debating machines is that even a low end machine in your shop is better than not having one at all.