If you are trying to stick to under a $1000 (minus the cost of a ball joint press) budget, then your options are also going to be limited. If you can afford it, look into the multi-process machines that can MIG, TIG and Stick weld. You'll be able to weld everything from aluminum to titanium. and everything in between. I have a Everlast 210 Ext that is TIG and Stick. And it is a workhorse. Not terribly expensive. My buddy has a Millermatic 211 MIG machine that is awesome. The miller stuff is kinda pricy but if you can find one in good shape used, they are worth the money.
While you are looking for welders, see if you can find a bunch of scrap metal to practice on before you start welding on the jeep. To get you started, watch some of Jody's MIG videos:
https://www.youtube.com/@weldingtipsandtricks -- he's been called the god father of welding, and for good reason.
Definitely do the ball joints yourself. Its an easy but time consuming process. I'd recommend an extra pair of hands when it comes time to line up the press.