Hello fellas,
I am a welding instructor and taught many basic welding courses at trade schools. I curently teach pipe welding.
To answer your questions, If you have never welded or have never been around it i would look into one of the courses, they are not all that much and you can get alot out of them. Safety/mach set up and the just of it. If you been around it then you could do alot of research on the internet and U Tube ect.
If you are going to buy a unit, start with the basic models, like a 110 volt mig welder for your basic garage work on thin materials. Plug it into the wall and your welding.
Most of these mach can handle up to 1/8" thick material, anything over that you need to bevel the joint and do multi-pass welds.
Then you get into gasless and gas mig welders. The gasless flux core wire works ok but if you use a sheilding gas with hard wire the weld is 100 times better and is much stronger.
Stick (Arc) (Rod) welding is alot differnt it takes alot of practice and skill to acomplish this, plus it is very hard to weld thin material with a Arc welder. I would not start with one being a newbi. This would be a step up kinda thing!
Oxy-fuel welding is ok for some things but it is dated, mostly used for cutting/heating steel.
Nowadays we have all the fanncy cutting tools and such.
Hope i have helped. Good luck to your quest and welding is great way to express yourself.