I have had really good luck with a small wire feed welder, using flux core wire. I have a Lincoln Weld Pak 100HD Wire Feed Welder. You can find them at Home Depot for about $300 bucks. It runs on 120volts, and can be plugged in just about anywhere you have a 15A outlet. It only weighs about 25 pounds or so. I have run several spools of wire through my machine. Works nicely.
I really like wire feed better than stick. Its just easier to deal with, especially for smaller materials up to 1/4" thick. In general, anything in this price range is really only good for 1/4" materials on a single pass. Thicker materials are going to require multiple passes regardless of stick or wire feed.
If you are going for a light duty machine where you don't weld all that often, wire feed may be a better option for you, even though it costs a little more. Stick welding requires a little more practice. Wire feed is sort of a squeeze and squirt metal approach. I find it easier to teach others as well. You don't have to master the feed motion. Fluxcore wire is also easier to clean up than stick.
There is a MIG option, which allows you to weld using a shielding gas. Don't bother with it. You can do about 99% of 'around the property' welding with just fluxcore.
I also have a Miller TIG welder, plasma cutter, stick welder, and oxy torch setup for all of my other welding projects. I still use this little machine for about 80% of my welding projects.
In general, if you are trying to weld something > 1/4", then you need to get more instruction on how to do it from a community college or tech school. This is the case no matter what sort of welder you end up with. Equipment in the categories you or I would buy can't generate enough heat to properly weld materials much thicker than 1/4". It also would imply a material that is supposed to support more weight or stress than welding a fender back on your tractor. In that case, it really pays to have had instruction on how to do it properly.
I took a great class at the local community college where I learned TIG, MIG, STICK, aluminum, gas, and brazing. I was able to use a wide variety of different machines and techniques. Great class, highly recommend finding one near you.