Do I understand correctly that I erentpayments.com allows ach debit allowing the landlord total control (tenant can not cancel the auto deduct from their account without landlord approval)?

Bank to Bank ACH transfer.

That way the head ache of evicting is in the sellers hands.

I have a lead of another student who is interested in renting a room who is in the same program as I am (medicine). 

You could encourage her to switch over to automated ACH payments with a discount perhaps.  

I'm in the approval process to accept ACH payments. 

We typically only deal with ACH but I would assume there would be similar rules for regular checks also regarding the time frame to return them.  

I'd suggest agreeing to waive the fee if they elect to pay automatically though ACH transactions.

Less heart ache and usually more repairable.

The more tenants, the more problems and damage and maintenance.So, for me - the ultimate would be a multi-family building next to a university with grad programs in law or medicine, with small studios.You might want to target your ultimate tenant - then look for properties that would work for them.