Working with metal is about learning how the heat causes the metal to shrink and how to correct the shrink.
Correcting shrink is easy, you just beat it some. Well some careful hammer on dolly work that you learn through practice. So the idea is to do welds that you can hammer properly. I started out doing this many wrong ways and then I found a book and bought some videos (which you can rent from smartflix).
A MIG welder will do a job, but having switched over to TIG I will never go back. The biggest mistake you can do is buy a cheap MIG welder. It is hard enough getting a good weld with minimal added material and if you buy a cheap welder then all the settings will always be between the settings you can set. See the problem with the MIG weld is you are always adding a lot of material. So before you can try to correct the shrink with hammer on dolly work you have to get he metal level. Even then the MIG weld is a bit hard and never quite levels our right.
A TIG welder is a wonderful change. You get this point of heat the melts the metal together, you just occasionally add a dab of a filler rod, mostly to add the silicon (I believe this is the right science) which helps the 'dirty' metal flow together. Since you add so little metal the area is fairly level and soft. It is a dream to correct the shrinkage with hammer on dolly work. The metal if very responsive and even crappy welders (like me) can get metal to be right and hard to find some of the weld line.
A lower cost option to a TIG welder is a very small oxy/act torch tip with low pressure gas. You will get more heat, but you can lay in a nice weld that hammers great. You must also you the right filler rod, there are rods for TIG and MIG and then there are rods for oxy/act. I know if you try the ER70S6 commonly used for TIG (and MIG) it is difficult to oxy/act weld. I have not taken the opportunity to get some proper rod for gas welding and set up my henrob torch to try.
As with most parts of restoration. Knowledge is key. You have to take the time to understand the metal and the welding process for best results. The right setup makes the welding easy and has a huge payoff in job quality, but it is not usually cheap.
FWIW, my TIG welder is a 60's vintage Miller 330A/BP unit. It is large and heavy. Working units are found on craigslist for around $600. They need 220V single phase (check the label) and normal house breakers will limit you to about half the output power. Even just powered on they will make your electric meter spin pretty fast, so keep that in mind. They still liked by pro welders, but they need computer controlled welders today to work with modern metals. So some of the older TIGs are available at lower prices.
Here are some examples of small torches.
Meco Torch
Henrob
Follow the link at the bottom. I have some metalworking hints as well as video titles on my website.