You can get enough out of a 110 welder if you use and implement the proper techniques. If you don't, then the integrity of the weld would definitely suffer. For example you could run .035 flux cored wire, multipass with proper joint fit up, prepwork, and cleanup to hold for what you need. Proper beveling and cleaning is a must as well as preheating the area to be welded with at minimum Mapp gas, or preferable oxy-acetylene would be much better. This would suffice for welding anything up to 3/8 thick materials. If you must weld in the vertical position make sure to do so uphill. I would look into Mig welding for what you have described. Tig welding structural components would definitely take a machine with 220v input and a rated output of at least 175 amps or higher.
As far as learning with mig/fcaw, there are tons of videos on the web that can get you pointed in the right direction, but the best way to learn is through practice, practice, and when that gets old practice some more, and show your welds to someone who can give you constructive criticism about how to make your technique better. The best thing to do is to enroll in a local community college course, most offer day, night, and/or weekend classes that give you the right environment to practice the right way. I'd be willing for you to post pictures of your welds on here and take criticism here, as there are many knowledgeable people on this board willing to help.
As for a first machine, the possibilities are endless. Get the most amperage outputs for whatever input voltage you can provide. I would definitely recommend figuring out a way to run 220v to power your machine, but if its absolutely not an option, get highest amperage 110 machine, and the largest diameter flux cored wire you can run in it. You will be able to run solid wire with shielding gas on thinner materials as well (.125"). Flux core will penetrate into the base metal deeper than solid wire, however pre-heating will help, and interpass and post weld cleanup is a must with flux core. Pick up and air needle scaler while you are shopping to clean the weld and to peen it, stress relieving the joint. I do not recommend welding suspension components with a 110v welder, but it can be done with a proper technique and understanding the limitations of the machine, and changing your welding style to account for this.
The biggest difference from stick welding to mig welding, is you cannot sit still and wait for the mig weld to build up, or the bottom of the puddle will be cold and will insulate the arc from the base metal, make a very weak bead. You must weave much faster with mig in order to keep the Arc slightly in front of the solidifying puddle in order to keep the underside of the puddle "hot". And whatever you do, DO NOT TACK-TACK-TACK,or trigger weld anything other than cosmetic sheetmetal.