@Ben Wenger, I just found myself in a similar situation. I recently purchased a triplex that was fully occupied. I sent new landlord letters to all of them informing them of the change in management and advised them how to pay rent, when rent was due, who to contact for maintenance issues, and upgrades we planned to carryout on the property. I also informed them that their rent would be going up and that, should they stay, they would be shifted into 1 year leases. However, I gave them 2 months before the rate increase and lease signings took place. This 2 month window gave them an opportunity to look for a new place if they couldn't afford the rent, but more importantly, it allowed me to get a read on the tenants before being tied to them for an entire year. Luckily I did because one of the tenants didn't pay rent, had too many people living in his unit and created non-stop problems for the other tenants. Because he was still on a M2M I didn't have to go through the eviction process. I simply served him a Notice To Quit informing him we weren't renewing his lease and that he had to be out within 30 days. (Your'e bound by the lease and/or state on the amount of time you have to give. Do your research!)
All in all it took a little longer than I would have liked but at least I wasn't contractually obligated to lease to him before I realized what kind of tenant he was. This also gave me the opportunity to renovate the now vacant unit and put my own tenant in at a higher rent than the original tenant was going to be paying.
I didn't collect a security deposit from my remaining 2 tenants only because they have lived there for 20 and 8 years respectively and their units were very well kept. That said, I will be collecting one from the tenant I place into the 3rd unit.
Lastly, don't be afraid to raise rents, your business depends on that income! And your tenants are probably expecting it. (Again, check your local laws on rent control. I am not an attorney)
Best of luck!
-MB