Housing in Ann Arbor is really cut throat because there's not much of it. So ideally you would start looking as a freshman when you're still in the dorms and would have your housing for the next year (or 3) lined up in the first semester, because everything goes quickly. If you do it that way and live with a couple people, your rent could be in the $400-600 range. I should also clarify that these are the houses on campus/really close to everything (which is what undergrads really want - as a grad student I care a little less? Idk)
Since we didn't know about acceptances until later in the year, we're late to the game. A lot of the places open right now are going to be ~1k if they're on campus. You can also try finding someone looking for a roommate which would definitely be cheaper, but a lot of the posts I've seen are only looking for someone to sublet their room for the summer.
If you can't find somewhere cheap on campus, I would recommend looking into cities off campus. Ypsilanti is a good place to look as it's a ~20 min drive and usually a lot cheaper. (Ypsi is also very LGBTQ+ friendly, if that's something on your checklist. It's also a college town for Eastern Michigan, so you'd still get a similar vibe to Ann Arbor.) I would recommend you plan on driving and parking in AA as little as possible because parking is horrendous and expensive. BUT the bus system is pretty great and the UM-specific buses are free for students. If you lived in Ypsi or somewhere close like that, you could drive to a free car drop off and take the bus into the city, which would be cheap. (I think Ypsi might also have a direct bus to Ann Arbor.)
That's what I would recommend for the first year if you don't find anything cheap on campus. If you're not looking for a place within a mile of campus, you'll have much better odds. Your commute will just go up to 20-30 mins, but once you're in the city you can use buses. Then, during your second year, I would gather up a couple friends in Oct-Nov and look for housing for your second year, and you would probably be able to find something in that $400-600 range on campus/close to everything.
To look for housing for next year, I would say checking Craigslist, the
UM Public Health 2018 Admits Facebook page, the
Ann Arbor Michigan Housing for Rent page, zillow/trulia/etc, something like Easy roommate or something about Ann Arbor roommates (I think Michigan has a site specific to that but I don't remember exactly what it is, sorry. It would probably come up with google though).
Apologies for this and future posts, I am clearly incapable of not writing novels
I didn't go to Michigan for undergrad, but both my brothers and many of my friends did, and I live close by and go there to visit friends often, so I'm happy to answer any questions I can about Ann Arbor/Michigan/Detroit/etc/etc.