Good names in welders would be Lincoln, Hobart and Miller. I bought a Lincoln 140 in the Home Depot version for $525 in 2011. I'm on my fourth large spool of flux core wire and it's still works well.
If you have good access to a 220V power source, a Lincoln 180 is still pretty inexpensive and will weld thicker metal easier than. 115v unit.
You can find decent deals on CL too but you would need to know more about what to look for.
I think you should spend some time at the university of YouTube and learn a little about the difference between the MIG process and using a wire/filler called flux core, which is what I have been using. Flux core is messier but it's cheaper, unaffected by the breeze if I'm welding out doors (all the time) and it will penetrate a little deeper at the same setting than if a gas were used for shielding.
Being a med student probably has your attention all tied up so buying a welder and teaching yourself to weld right now might not be as feasible as simply saving money until you have enough to buy a good bumper. Other options might be; finding a good used bumper that you like, customizing your stock bumper or forgetting about it all together and focusing more on genetics.