Negotiated price down 10K even with a multiple offer.

You may not like their current deals/offerings, but I would call each of them and let them know what you are looking for - essentially your "buy box."

Now you might be like Joe, know rents for a couple of neighborhoods and can quickly estimate expected cash flow from properties pretty quickly (that's what I do as well) but you still need a screening rule so you invest minimal times on properties you will never put an offer in on. 

They're offering a few thousand more than asking and will also pay agent fees.

Yes, but highly unlikely:(Anaylsis process is pretty simple.To determine what to offer on a rental property:Determine reasonable market rent, NOT the highest!

Start where you are most comfortable.

On market & offered asking price How did you finance this deal?

You also want to know if the Bank/Lender offers a less than 1.00 DSCR option in case the rent schedule comes in light. 

Find out what works for you and your team on smaller deals then scale up once you start to get comfortable with multifamily. 

So think about what's comfortable for you.