I poked around the web, and for hobbyist welders there seemed to be consensus for getting a Miller for MIG and a Lincoln for TIG (the Miller TIG is good, too, but the Lincoln was a bit cheaper). I bought a Lincoln 180 TIG and have been very happy with it. The arc is easy to start and very stable, even if your spacing to the work varies a bit. I can weld 1/4 inch steel with about a 1/3 duty cycle (you need that to cool off your hands anyways!), 1/8 inch or thinner is continuous. I'm not a great welder, but you can see some of my welding projects, for my gas and electric cars, on my web page
http://ExplodingDinosaurs.com .
Safety Caution: You need a special helmet for TIG. TIG is much brighter, so you need a darker eye piece. TIG also sunburns you very quickly. You need to wear a leather jacket and gloves (the light will shoot right through cloth). My sleeve pulled up once. In 2 minutes of welding I got a sunburn -- the pain took a week to go away.
There are special gloves for TIG -- they are thinner, so you can feel what you are doing better.
One caution is the really cheap TIGs are not computer controlled. The arc would be hard to start and maintain. I was also warned more than once you get what you pay for and to avoid the cheapy, no-name TIGs. Another trick they'll pull is to quote specs for a really low duty cycle (something like 180 amps, but only at a 10% duty cycle).
Final suggestion is to get around 10 of each size of electrodes. They are pretty cheap. When you contaminate one by touching the puddle, it's nice to just grab the next one rather than stop everything to regrind the tip. Also be sure to get a big enough tank so it fits safely in the machine. My first tank was too small and I had to be careful it didn't fall out below the retention chain. Don't get too big a tank, either, it'll be hard to pick up and put in a small car. My tank is about a meter high but lasts for several projects, I only refill it about once a year.