Ok...I welded for a living for 17+ years...went to school for welding, held a few certifications years ago but haven't welded for a living in over 10 years. I'm still in manufacturing at the management level (plant manager with 5 supervisors and 92 hourly under me). We have a variety of welders including robotic. I have also restored a few cars at home and currently own a couple welders myself. My point? I think I'm qualified to answer the OP question.
The Lincoln vs Miller debate is the same as the Ford vs Chevy debate. Personally, I like Lincoln for GMAW (Mig) and Miller for TMAW (tig). I have owned a Lincoln 255c, a Miller Bobcat 250 and I currently have an older Miller 210 with spool gun and a Hobart 140.
For automotive and home shop use, get yourself a 140 size machine. Brand doesn't matter as long as you stay with the three mentioned (for US, esab or others for non-US). Go for the gas hookup. Flux-core on a little machine is fine and great for what it is but you will be much happier with the 75/25 gas. I typically use 0.023 or 0.030 for automotive sheetmetal and .045 for bigger stuff. You can buy new for about $550 or off craigslist for $300+
If that works out and you want to go bigger or your budget allows it, go for the new Lincoln mentioned above. I have heard great things about it. I may pick one up myself.
Take a welding & metallurgy class at the local vo-tech center. You can self teach with youtube but there is a lot of bad info out there. Everybody and their brother can weld but few can do it well.