JBerry, I couldn't have said that better myself!
Just remember with a fluxcore wire you need to change the polarity from electrode posative as with MIG, to electrode negative for fluxcore wire. The "ground" clamp becomes posative. From how you speak I know you already knew that, but this was for Axilleas information.
I too run a small 110 vac Lincoln SP-135-T which would do about anything a home weldor would need. Hobart also has a very fine 110vac machine called a Handler-140. This is a better machine than the Lincoln IMO. I own both, and the Hobart can be had for less money than the Lincoln through outfits like www.northerntool.com for example. Both are MIG (GMAW) capable machines with regulator,guages, hose etc. included, but can be used as fluxcore (FCAW) welders by simply changing the polarity, and eliminating the gas bottle and related hardware.This process allows you to weld in the wind outside, where the MIG will not reliably.
Axilleas, Do NOT abandon your quest! "Welding" is just not the "process" you need to use for this application in my opinion.
If I wanted to join thease types of pieces, I'd be asking the guys like JBerry that are doing it.
My Dad was a jewelry fabricator and had a natural-gas torch to melt the silver. I don't know anything else about it other than it provided a very clean flame. I think that oxy./acet. would be too dirty and too hot for this but I may be wrong.
If you want a basic weldor, I would highly recommend a wire feeder. Just buy a good one from someone like Hobart,Lincoln, or Miller.
Prices for a commercial grade 110 vac machine will run between about $500 & $700.00. The ones you can buy at outlets like HD are NOT commercial grade machines no matter what name is on it. They typically run a couple hundred $ less. I would never buy a used machine that I couldn't try out, or from anyone that I didn't know. Good luck! Q.

edit; TIG is as JBerry said, is just like welding or brazing with a torch in one hand, and a rod in the other. The differance is that the "fire" is an electrical arc thats heat can be controaled by a foot pedal. The electric "torch" also delivers a shielding gas to the weld. Differant metals require differant shielding gasses and rods. Almost any aloy can be welded with TIG as long as the wind don't blow.
MIG feeds a solid wire (the rod) and shields the weld as the TIG does. TIG is the most accurate of the two.
FC is a wire feeder that is just like the MIG, but has the shielding gas (flux) inside a tubular electrode/wire, and can be used anywhere a standard welding rod could be used, but typically burns hotter than MIG due to the blanket of flux that lays on the weld, and a lack of cooling gas blowing on it. This is getting pretty complicated but I think you may have a better idea what the differances are.