I would use only TIG welding only, if it was mine.
MIG welding is used a lot on mild steel, however, I'd classify MIG welding as "operator sensitive", in other words, you can make a big mess in a hurry, and weld quality may suffer in a dangerous way. You could have more weld defects than you can shake a stick at, if your skill level ain't up to the task.
Rouse