We pretty much got everything we wanted in a tenant.At minimum get them to provide a co-signer with STELLAR credit.  

To answer one of your questions regarding putting the brother on the lease as a tenant and not a co-signer - if you did that, then he would be a tenant, and he could move in.  

Here's my issue, with this delicate situation I am going to have her give me all her son's SSI information and put him on the lease as a co-signer.  

One of the 4 will have a co-signer.  

The mom's credit score is almost 700, and she talks very sincerely and looks eager to move in.3.A group of 4 college senior female students and a co-signer who is the father of one tenant. 

But, hey, the co-signer probably paid their rent every month just to be sure they didn't move back home LOL.If you take a co-signer, be sure they're also only on a month-to-month agreement, so you can kick them out for all and any other reasons.  

I want a good tenant, in order to collect from a co-signer you must go to court.  

Lately, several potential tenants whose income didn't meet the 1/3 guideline (monthly income should be 3 times the rent) have offered to have a co-signer.

And a large part of investment management is understanding and minimizing risks associated with your investments.If you're not quite sure about a particular tenant, to address your risk you can (1) ask for a higher security deposit, (2) offer a month to month lease, and later be willing to convert to a longer 12 month lease if both landlord and tenant agree (makes it easier to evict in month-to-month lease if necessary), and/or (3) (if income or credit is the issue) ask for a co-signor. 

Must have good current and past land lord refernce, or I require a co-signer or double security deposit.