Do I just approve the first creditworthy person suggested to me, or do I let the other college students who are living there now have a say who replaces the old person on the lease?

How credit worthy is someone with a 615 score as compared to a 675, for instance.  

Will,  who on earth would offer this guy a loan, he must be the least credit worthy borrower on the planet !!..  

In general, lenders are typically opposed to loan assumption because they originate mortgages with terms based on the creditworthiness of the original borrower.There are also challenges involved in determining whether or not a new borrower can safely assume the original debt, and many lending institutions are simply unwilling to take on the risk.

If the not creditworthy tenant were to default on payments you would be able to go after the cosigner for payment, and the cosigner's credit would be on the line if payment were not made.

In some places its fine, but in others like TX its pretty worthless.After one has clean title and if the property is in an area the recognizes Quitclaims to transfer property, then one looks at the $ and credit worthiness of the LLC.

As @Bruce Petersen alludes to, for MF investments expect to have an in-depth inquiry to your finances and experience.Multifamily loans require a more detailed underwriting process than single-family loans due to the complexity of the collateral, the borrowers and the underlying transactions....careful underwriting is required to confirm a borrower’s creditworthiness and ability to successfully operate the apartment property that acts as collateral for the loan.

LOTS of credit worthy tenants looking for NNN leases and the rates are very good for land/property owners.

So if I'm going to move and wholesale and/or rehab in another state in 2 years, you're saying that I might be able to take my LLC with me (aka keep the credit-worthiness of my TIN?)

We have hard criteria (credit worthiness, criminal record, etc) but they have to pass the PITA test first.