I do not know how big of material I will ultimately be working on but to start light stuff mostly. I have some Oliver flat top fenders that I cut old steel out of and will be wanting to weld new still back in. Ground off all the material around the parts to weld and they are all nice and shiney but I hear what you are saying about the repairs. I think I will be doing 80% new stuff and 20% old repair. MIg still the safest bet you think?
You have the right idea about cleaning up the stock before welding on it. This holds true for stick rod also. Folks spout off that you can weld rusty, dirty steel with stick but not MIG. Well that may be partially true, you can weld dirty steel with stick and MAYBE if wont fall apart, but stick welds suffer from unclean welding just as MIG welding does. Just because you might make it glob on and hold two pieces together doesn't make it right to do regardless of the process used. Cleaning the parts first will make welding them 1000 times easier!!!
Saying that, MIG might be your easiest process to lay down a bead with but there are other factors to make it right. As ShieldArc says, cold lap is notorious with MIG welds and come mostly from not having the machine set hot enough (or too small of a machine). Another factor is not manipulating the gun to tie the edges in properly when running a bit cold on thin materials.
There is a bit more to MIG than just pulling the trigger on the gun, even if the machine is set properly but a beginner can put some nice looking beads on metal with them. MIG is likely the most expensive process for the home owner to run, the machines are expensive and the CO2/Argon mixed gas is expensive. FCAW (fluxcore) is a bit cheaper as you can run it without gas although it does much better with gas shielding. I prefer stick rod for my home repairs as it is the most versatile of all processes, electrodes are fairly cheap, welding machines are much cheaper than a large capacity MIG.
I would recommend you getting a 250 amp (min) AC/DC stick rod machine for your uses. It takes some acquired skill to learn but it isn't rocket science to learn to stick rod and with minimal electrode stock, one can weld just about any material found on a farm. E6010 or 6011, in 3/32 and 1/8" sizes will weld about anything that you have. I also stock 3/32 and 1/8" E 7018 electrodes as they are a bit more ductile and a lot stronger than the 60XX rods but are a bit harder to start and weld with.
With the AC/DC machine, you can later add a TIG torch and argon regulators for a couple hundred bucks for that delicate work that stick just cant do easily. TIG welding requires 100% Argon shielding and tungsten electrodes, neither of which are cheap, but the tungsten lasts a long time. The Argon gas will last a bit longer than the mixed gas would for MIG as the nozzles are much small so the flow rate isn't needed to be as high.
Best advice is to find a local community college that has a welding course and get some preliminary instruction. It is the cheapest way to learn to weld as they have all the different machines, furnish all the supplies other than welding hoods and gloves and usually have a knowledgeable instructor to teach you the basics of welding and metallurgy. Knowledge of Metallurgy is a very necessary in welding as you need to know the properties of different metals, how they behave to heating, cutting and welding. You wont learn this from just burning rods in your shop.