Reddit reviews Welder's Handbook: A Guide to Plasma Cutting, Oxyacetylene, ARC, MIG and TIG Welding, Revised and Updated
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I think a good first step would be to read a general book like this one: That will give you a solid, fact-based, overview of all the main welding and cutting processes.
After that you could buy a high quality stick/buzzbox/SMAW welder for $300-$400, it will last forever and allow you to weld a fairly wide range of steel things. The downside is that stick welding requires a certain baseline skill level and can be frustrating for a beginner.
MIG welding is the easiest and probably most common welding process, though you will have to spend a bit more to get a decent one. When people describe welding as a "hot glue gun" MIG is what they're referring to.
Many community colleges have basic welding classes, "Maker" places too, otherwise find that guy in your neighborhood who is always working on cars. Most people don't use their welders all that often and like a chance to get them out and stick some metal together.
I'm not an expert by any measure but I've found Richard Finch's Welder's Handbook to be aptly named.