Private lenders tend to focus more on the value of the asset or project rather than your credit score or financial history.

For financing, you might want to consider reaching out to local banks or credit unions.

Also credit score 680 with no missed payments over the last 2 years and also check their criminal report just to make sure you know who these tenants are, as the eviction process in New York city is very long and expensive. 

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

As a landlord you can report payment and non payment to the credit bureaus without a judgement.

When you go to a Bank or Credit Union, they can only offer you what products that bank or credit union offer.

Cleveland currently has one of the lowest price/rent ratios in the Nation, with the average home price being $107k and the average rent being $1,416/Mo.

As well as 3 credit cards which so far have not cooperated and synced with Quickbooks which takes some extra time each month.

The only example I can think of is that I asked an applicant questions about their credit report.

You can do a duplex though, which might not be a bad idea.With your credit score, conventional might be a good choice, you only need 5% down for 2-4 units if you live in one.