Etch,
I think that your welder will be able to weld your bucket hooks, although you will be right on the ragged edge of your 120V machine's capability.
Since you haven't welded before, I certainly wouldn't make the bucket hooks one of your first projects. If you need them attached soon, I'd highly recommend that you get an experienced weldor to do the job for you. You don't want a hook to come off and possibly hurt someone or something because of an inadequate weld... which, is one of the MIG's little "gotcha"'s... It's very easy (until you get some experience and know what to look for while welding) to make a very nice, pretty weld on something like a bucket hook that won't even hold a potted plant. And, the larger the material that you're welding (like your bucket hooks), the easier it is to have this happen. The best thing you could do is to take a welding class at the local community college or at least get some instruction from a knowledgeable weldor. That is the biggest favor that you could do for yourself with your welder. And, practice. Get some good instruction, and practice what you're taught.
And don't let the fumes scare you, it isn't necessary to dress up in astronaut suits or to have a hood with forced air respirators and all that stuff like some members here believe

. Just use your common sense. Don't weld in an enclosed area. Be sure there is good ventilation. The one exception is when welding galvanized steel. Zinc fume poisioning is very real. I haven't ever heard of anyone dying from it, but if you ever get the "fever" from welding galvanized, you will wish you were dead. Avoid welding galvanized if you can. If you do ever have to weld it, set up fans to blow the fumes away from your work area, and do it completely outdoors if possible, not in the shop.
Try to clean any paint off of the material you're welding before you strike an arc. With your MIG, that is a REQUIREMENT... CLEAN CLEAN CLEAN is the name of the game with MIG... they do not like dirty metal at all. They are not like a Stick machine, where you can weld right through rust and paint and whatnot and get a good weld... with MIG, it has to be clean before you start.
Good luck with your little Lincoln, and welcome to the welding world.