Apart from the standard legal terms of a lease agreement, is there anything that I should consider adding to the lease that would not typically be already written in the contract?

There are noise standards no matter your mental issues or the issues of your child.It is wrong to decide one tenant can be destructful to another because of a medical condition.

I don't have anything to offer with your question beyond what everyone else has said but I just want to let you know some general rules with foundations:1. crawlspace - cheapest to repair, good for plumbing because they can run underneath the house and easy to repair, bad for really cold days, pipes could freeze, some people complain about moisture in crawlspace and tile cracking but that's a long term issue and you may not have to deal with that and if you do, just lay LVP2. slab - second cheapest to repair generally, worst for plumbing because to fix, you have to often remove flooring and drill into the concrete to fix leaks and I've had a house that I played whack a mole with an active leak3. basement - most expensive to repair, okay for plumbing, but your basement could leakIMO crawlspace is the gold standard for foundation for rental investments in older properties (older than 1950s).

We like the gold standard of FDIC insurance for each account. 

I hope I don't come off as brash, but my first instinct is that the rent is either too high or the condition of the unit is of lesser standards to your competition.

True, first in line who qualifies is standard practice.

Christian, I think Eugene may have made a typo. 100% of first month's rent for using an agent and putting on mls is pretty standard.

Nobody who knows the market would do that, but appraisers are held to standards which restrict them from determining actual market value.

Or can I connect with someone who already has one up to legal standards in the state of TN??

Not being familiar with your area’s standard forms I’d say that 99% of the appraisal contingencies I’ve seen either expire automatically (the buyer waives it) or require the buyer to give notice of low appraisal at which point the deal is either renegotiated or cancelled depending on what they say in their notice.