If you're main concern is body work, frame repairs etc go with a wire feed, using a solid wire, gas shielded, not flux core. If you're a novice (no insult intended) it will be the easiest to pick up as well it's the most 'forgiving' as far as fit up, ability to weld to less than sound body panels and ability to fill holes, gaps etc.
You can get good results with a 150A machine which will run off a 50 amp circuit but check the welder specs first to confirm. I've got a 250A machine running off a separate circuit with no problems, (yet anyway), if you're after economy CO2 is the cheapest gas to go with ( be sure it's compatable/recommended for the wire you're using) use an .023 or an .030 S6 wire .
It's not a 'regular' wall outlet as such but it can be installed by any competent electrician.
By your third question I assume you're not a tradesman at least as far as welding goes, there are so many variables as far as looks, size of bead, base material condition goes that I wouldn't even attempt to  answer that.
Be warned, there is more to frame repairs than 'sticking' it together, you have to be sure that you are not compromising the structural integrity/design of the vehicle. You would be leaving yourself open to a lot of grief attempting to repair someting you're not familiar with. I would you suggest that you get some training first, be it a course at a trade school or whatever. There are some things that just can't be repaired, safely anyway ...Mike

Stick welders (Shielded Metal Arc Welding process)can be used for most welding applications, including automotive.  It is probably the most versatile of the processes for ease of use, portability, availability of supplies, and initial cost of equipment.

Having said that, you must also recognize that other processes are better for certain applications, though the stick process will suffice.

Be careful using any welding process for automotive structural repairs.  Autos are subjected to significant fatigue cycling which is one of the reasons you see warnings on truck frames "DO NOT WELD or FLAME CUT FRAME".  There's a good reason for this as vehicle frames need more flexibility than welding often affords.

Regarding the power source...You will typically need at least a 220/230 volt, 30 amp circuit to supply a small "hobby type" welding machine.  This is comparable to an air conditioner or range circuit in your house and is minimum!  Preferably you will have a better power source (230v, 200 amp service)for your welding.

For your third question, the size of the "bead" is only one of several variables that affect the integrity and quality of the weld.  While size is important (ain't it always!), proper selection of filler metal, speed of deposition, machine settings, proper fusion and solutioning of weld and base metal, weld profile, and technique are all important to quality welding.

I would suggest you consider taking a welding course at a local community college or extension education program.  This will give you a good mix of theory along with practical application.

Good luck.
Ron