As far as I know, nowadays most bikes (not the extra cheap neither the extra fancy) are TIG welded. If I'm not mistaken, MIG is used for lower end aluminum frames.
I have made a lot of hacks and fixes to steel frames (including building a recumbent frame from an old, already cracked, MTB frame), and always used TIG weld, with excelent results, either durability and aesthetics.
The main difference between TIG and MIG is that, with MIG, the electrode and the deposit material are the same (consumable electrode), while with TIG you have a non-consumable tungsten electrode and a consumable, handheld wire rod. Not only the tungsten electrode has a sharper and more precise point, but also it is more probable to the shop to have wire rods from different (and more suitable to your bike) steels, than it is for them to have multiple large rolls of different MIG electrodes.
So, I recommend you to look for TIG welding instead of MIG welding, at least for steel.
Hope this helps!