You just have to be careful because Craigslist and Zillow hide your identity where fb marketplace will not.

I might also consider staggering the leases if all the units are identical.

If you get to identical tenants, you must offer the place to the first applicant, offering them a defined deadline to pay all fees to you.

@Jay Maranan just an FYI, my primary property is 5 stories, of which almost all the carpet in the units has been removed(90%)...the original flooring is beautiful oak, that was original installed over 90 years ago, however, the units that just have the carpet torn up, sanded and stained the original flooring are much louder that the units, that I lay down subfloor, underlayment foam, and new floors over the original solid wood(I know it is sinful to purists, to not refinish the original wood, but it cost more, takes longer, is louder, and less isolation of bugs, and leaves some of the earthquake retrofit hardware exposed, if I do that) ....BUT, with carpet and/or wood floors it will be noisey...that's why the 5th floor are the "PentHouse" units, since no upstairs neighbors, even though identical layout to the below units, they can demand a bit of premium, especially if your new tenant has lived in apartments before.

My situation is alarmist identical to yours and so far it has worked out well for me.

In this age of identity theft I would NEVER rent to someone I have not met eye to eye. 

Remember a lease does not prevent a tenant from vacating when ever they want and the terms of the lease are identical regardless of term or M2M.

And then how would I handle verifying their identity and all that prior to signing a lease?

I was suckered by one of the first replies , which was identical to the verbiage in link below but they used another name.  

In CA they charge $100k more for the same identical plan.