Yes, you should have a lease. That will clearly state all the rules and reduce any liability for you. You should also do a thorough screening of all applicants (ie, credit history, employment, references, etc.) For me, this part is most important as you do not want to be stuck with a bad tenant. You can google online or even go to http://www.westsiderentals.com
to find a free lease agreement or rent application.
Definitely ask for a deposit, it's like "insurance" (ie, tenant doesn't pay rent or tenant moves out and makes damages, you can take out of their deposit). You can ask for first & last month's rent. But keep in mind, you may have to be flexible. You might be in a situation where no one can afford 1st/last month's rent, deposit, moving cost, etc. so you could work out a payment plan, etc.
This is just the gist, but I hope it helps. Good luck.