Older buildings have lots of skeletons and aches underneath, not visible on the outside.

The large muscle movements seem rather well covered, but the finer muscle motions are less covered and that’s where you will need some counsel from an SDIRA Attorney and from a good Custodian.

Things I'm looking for: ability to accept ACH directly and circumvent Apartments.com or other 3rd party website; no fees; interest.

I use TenantTech Not sure if they have e payments as I use ACH but they do have everything else and it is cheap.

It's too late for this install but if you are re-tiling the same space with a tile that is less than 3/8" thick and the existing tile is reasonably level, you can use a product called muscle bound (Lowes) or simple mat(Home depot) instead of thinset and tile right over the old tile.

We use Rentec Direct… costs between 1-2$ per door per month and they front your ACH payments the very next day in advance of them fully settling with no percentage fee for any of the rent collection services.  

We use TenantCloud with ACH and a PO Box for our tenants that use check or money orders 

Some banks have good online banking with cheap wire transfer or ACH.

Does TenantCloud accept standard ACH payments for collecting rent?

i use Myrental.com for screening (and it can integrate back to tenant tech) and i use my bank for rent collection via ACH and quickbooks for accounting.