So I have this awesome friend who is learning welding. She offered to teach me when she finishes school for it. She is very smart and learns quickly so I have no doubt that she will have it mastered in no time.
That's awesome.
There is however, a
very big difference between "learning" and "mastering".
I am going to want to weld aluminum, cast (aluminum, steel, iron), and steel. IE cylinder heads, engine blocks, roll cages, etc. I know there is a fair amount to it and welding cast is damn near impossible.
Welding cast iron is sometimes doable. Welding cast aluminum is sometimes doable. Welding cast steel is sometimes doable.
A lot depends on the
exact alloy of the casting, as well as the 'purity' or 'quality' of the casting.
A poor quality, porous, oil-soaked, 'mystery-metal' aluminum alloy casting (hmm, like a Chinese no-name 'motorcycle' crankcase cover, for instance

) may be darn near impossible to weld. Or weld well. Unless you want to include J-B Weld as a "welding" process.
Welding plain low carbon mild steel is usually very doable, depending on the exact welding process being used and the welding parameters being used and the
skill of the person doing the welding.
Trying to weld some 22 gauge sheetmetal with some 1/8" 7018 electrodes with the SMAW (aka 'stick') process would take a welding god to be able to do -that-.
Maybe Hephaestus could do it. Being a god and all.

Although he usually seems to prefer the forge, anvil, and hammer for most of his work. At least in the paintings.
I believe my wall outlet is 15amp but, may be 20amp. It is on a fuse circuit not a breaker (old house). 120 volt 60hz American standard A/C.
That limited power source limits the welding choices to 120V input power machines. Or maybe some of the 'newer' 120/240V dual input voltage machines (Lincoln PowerMig 210MP, for instance).
So what would be a good arc welder that is capable of doing those kinds of welding. Obv with all things I would like to do it without breaking the bank and I am thinking a used unit. At the same time reliability of the device and not setting my house on fire (attached garage) is important. I have no qualms about maybe taking apart a unit and cleaning it out / replacing parts if need be to get a good functioning unit. I also wouldn't mind renting one just to learn on till i can find a good quality cheap unit.
Hopefully the machine itself would not be a fire hazard. Dealing with molten metal from the welding process is usually the higher fire hazard.
Info about my house and electrical routing:
I also do not have high amperage service I only have 120amp service and the fuse panel that powers the addition and garage is 50 of the 120amps. It has no open slots left in either panel.
I am guessing it will take roughly $3k-$5k to run a new line from the pole and install a new panel in the garage, install conduit/boxes/outlets and probably $500 to update the small fuse panel in the house to a small breaker box. If I have to install a new box I would probably have it setup for dual or tri phase if needed.
Dude, you need to read and learn about electricity a little bit. 3-phase to a house is usually NotGoingToHappen is most (all?) of the US. Even though the typical power distribution lines running right past your house are 3-phase, the utility companies typically do NOT run 3-phase power to a house.
And although there is such a thing as "dual phase" electric power, you don't have that either.
In your typical US house, you have single phase power. 240V AC from hot leg to hot leg, and 120V AC from either hot leg to neutral.
https://en.wikipedia.org/wiki/Split-phase_electric_power
https://en.wikipedia.org/wiki/Single-phase_electric_power
https://en.wikipedia.org/wiki/Three-phase_electric_power
https://en.wikipedia.org/wiki/Two-phase_electric_power
So if I could avoid that it would be awesome. Especially because I have been out of work for a month and probably wont be back in for another month if i still have a job.
Out of work for a month already, with another month before you -might- even go back to work?
Unless you really have a nice emergency fund (financial cushion, rainy-day fund, etc), don't worry or even be thinking about redoing your house's electrical panel and buying a welder. IMNSHO
All that out of the way, or at least addressed in a semi-perfunctory manner, what you 'want' does not really exist.
A
to weld
aluminum, cast, and steel
all running on 120V 15 amp input power.
The closest you'll come to that unicorn machine AFAIK would be something like the Lincoln PowerMig 210MP. Which could maybe let you start doing some welds with 120V input power, until such time as you got 240V input power available for the welder. That specific machine can do GMAW (aka MIG) or FCAW on steel, or on some aluminum with the optional spool gun, and DC SMAW or DC touch-start GTAW (which pretty much means steel, regular or stainless only, ignoring the possible but not 'easy' DC GTAW on aluminum).
Good quality, but not cheap. Base unit is around $1200 list (you missed the Lincoln rebate/incentive of $200 by a few months) which gets you wire feed ready (GMAW or FCAW-S) and SMAW ready (has the electrode holder for SMAW, the work clamp aka 'ground' is already there), the spool gun for aluminum is about $200, the GTAW kit is another couple hundred, add in some shielding gas cylinder(s) for GMAW or GTAW (different gases used for the different welding processes), add in a decent welding helmet (maybe $40 to $300 for a nice one) and some welding gloves ($20 or so) and a welding jacket (maybe $20 for a fire retardant cloth one to about $100 or so for a leather one) and some angle grinders (yes, plural

) and you are probably around $2k all up.
Your friend is going to welding school? And is willing to teach you some welding? Learn at her place (she'll probably have a welder, since she's going to welding school and all). Bring your own gloves, maybe a low-end but decent helmet, and some food and refreshments for her (pizza and beer, or sandwiches and iced tea, or whatever
she wants) and maybe offer to pick up or reimburse some of the consumables (electrodes, whether wire for GMAW or FCAW or sticks for SMAW). Learn and start to figure out what you actually want to be able to do or even
can do for now.
A dream of a full-up any process and any material welding fabrication shop is cool and all that, but it doesn't really sound like you are at a point to really make that happen just yet. Because of money, learning welding, electrical power, etc.
Go read up about welding at the Miller or Lincoln or ESAB websites. Theory, history, safety concerns, tips, examples, projects, FAQs, etc. Then go to those companies YouTube sites and watch their videos for some more info. Then go to some more welding info sites and/or YouTube sites and get yet some more info.
http://www.millerwelds.com
http://www.lincolnelectric.com
http://www.esabna.com
http://www.weldingtipsandtricks.com
Come back in a month or two after doing all that and digesting it all and let's go on from there.