Kerrytown and Old West Side would both be great choices! A lot of grad students and young professionals live in Kerrytown--it's close to a lot of stores and coffee shops and the Ann Arbor's farmers market. You'd still be close to all of these things on the Old West Side, too. Burns Park is also very nice--closer to campus it's occupied by undergrads, but as you move south it's quieter with more families--a lot of professors live there. There aren't really any "bad" areas in Ann Arbor, though. Choosing a neighborhood depends a lot on what is important to you. If cost is a concern, for example, you might try looking a little farther from campus, around Briarwood Mall etc. (Nowhere in Ann Arbor is going to be cheap!) If fitness is important to you, check out what gyms are close (UMich gyms are IMSB, CCRB, NCRB--IMSB just got renovated, the other two need some work) or if you're a runner an apartment close to the Arboretum might be a good fit. If you're looking for quieter areas, probably best to avoid South University or Tappan neighborhoods--these areas are loud and lively, filled mostly with undergrads, sororities, fraternities. The Elbel/East Packard/Yost neighborhoods are also home to a lot of undergrads, but again, this shifts as you get farther from campus.
I'm not sure about smaller places vs. apartment complexes, but you could start with CMB and J Keller Properties--both have good reputations. https://www.scribblemaps.com/maps/view/UM-Neighborhoods/