DO NOT RENT SIGHT UNSEEN!!!! I cannot emphasize this enough. There are complete rat holes here. The city just passed a rental property ordinance but it hasn't gone into effect yet...you could end up with a really crappy place if you don't come here in person to find a place to live.
I know several KCOMers are coming to town this spring/summer to look. Waiting until the last minute could leave you with very few options since you are competing with Truman State students as well as KCOMers.
If you absolutely cannot be here early to find a place, then you may want to go through a local realtor (Century 21 is the best, IMO). There are reliably nice apartments/condos to rent such as Woodwinds and MedRow, but beware of any houses near campus...they are often very slummy and barely standing and you'd be surprised at the rent- $1000 for a 4 bedroom house that has no air conditioning and holes in the floor, for example. You might think that that's a bargain if you find 3 other people to share it, but you could find a nicer, smaller, newer place a little farther from campus for $500 that still has room for 2 people. (And remember that KV is a SMALL town, so farther away from campus is only a mile and a half).
As for rental pattern- spring is THE time to find a place for the fall. You shouldn't have too much trouble waiting until June, though. If you have a pet or a family, start looking very early as suitable places are difficult to find.
Good luck!