I get the distinct feeling that you have no idea just how difficult of a project this is going to be. Inverters require meticulous attention to detail, especially high powered inverters. One thing just slightly out from perfect and the whole thing goes bang in an instant.
If you want a welder just buy one, if you are on a budget you can buy used welders, sometimes for not a whole lot of money.
If you want an advanced engineering project then go ahead and try to build one, just realize that you will spend more money on parts and almost certainly get inferior results to the cheapest Chinese welders on the market.
Also how experienced are you at welding? MIG is one of the easier ones to learn but it still takes a great deal of practice to get good at it.