Really, living downtown is not so hot. My girlfriend has done it for 2 years now and constantly complains. Generally, it's just a pain. There are no good grocery stores. Need a Home Depot? Get in your car and drive to the suburbs. Ditto for any type of shopping or movie theater. There's not a great selection of restaraunts or any ammenities for that matter. What you make up in convenience by being right by UDM you'll lose in the sheer inconvenience of everyday life... Detroit is really that dead, and I sadly know from boatloads of experience.
I would live in the south suburbs right off a highway (I-75 or the 9-4) and do the 15-30 min commute in each day. Typically, you won't be in/would be able to avoid rush hour traffic, especially with a short commute, and it would make your life actually a lot more convenient/enjoyable. If I were you, I'd get an apartment in Ferndale or Royal Oak -- since these areas have a "main drag" so-to-speak there's a lot of conveniences all within a short drive or even walk of where you live, and UDM's campus is only a quick drive down I-75. Sure they're a bit expensive, but you could find something reasonable a little bit off Woodward/Main Street.
A final note about living downtown: I don't really want to bring this up, but just about everyone I know has dealt with crime in Detroit -- many cars stolen, windows broken, and sadly, a few people being mugged. I really hate the fact that my girlfriend lives there, but she has to cause she has no other options really. If you must live downtown, live on or as close to Wayne State's campus as possible. WSU's crime rate isn't that bad; it's actually comparable to MSU but with a lot more carjackings. I hate to bring this up, but it is sad yet true. I used to really believe in the city growing up, but my experiences over the last two years have proven that a lot of it's bad reputation is well-deserved.