As an initial screen look for properties that will bring in 1-2% of the purchase price in monthly rent.

Yes, we get plenty of people applying that don't pass our requirements or are currently getting evicted, etc. but it is pretty easy to weed them out with a quick online pre-screening form and a check of the Rhode Island Judiciary website.  

but really I can find you a tenant in 24 hours too..... the concern is not only speed but the quality of the tenant they place.... so I would expect a company that makes that promise or offers a speed guarantee to have another guarantee that focuses on the quality of tenants they place such as a placement guarantee or eviction protection, etc.In our opinion when hiring a PM you should be looking for 3 things, 1) the speed at which they can find you a tenant (turnover, marketing, etc), 2) the quality of tenant selection (criteria, screening, etc.) and 3) control and oversight of your investments (inspections, leases, vendors, tenant relations, etc.) ---- and these should be STANDARD in some form or another within your PM program, of course they can charge for additional items above the standard that is fine but a reasonable package that includes all of the above should be included within your program. 

@Michael EalyYou know my strategy, Michael, poking around ugly places to find the pocket solid C'class neighborhoods in borderline D'class areas, buying SFR at D'class price, renovating to solid C'class standard, renting for low market rates to very-well-screened tenants looking for long-term housing.For various tax reasons, the entire area I'm investing in is getting a significant increase in its public budgets, municipality and school district.

I did screening through Zillow Rental Manager and got my rental agreement from BP.

The advantage of this approach are:As an owner occupant, you would be eligible for a high-ratio, insured mortgage (95% LTV for a SFH or duplex); you would have "roomer"s living in your own house, so it is easier to evict a poor tenant {from time-to-time one is bound to get by your screening}; since you live in the house, it is pretty easy to be the coxswain and keep things tidly and the crew in-line; if you were in New Brunswick you would also benefit from the owner-occupant exemption from the provincial portion of the  property tax (about a 40% saving).The obvious disadvantage is that you will be sharing your living space with your tenants  {find a home with an en-suite and you'll have a private bath}.You still need to do your homework.  

I do have another question for both of you.Have either of you ever had a prospective tenant who met your screening criteria but there was something about them that gave you a bad feeling?

Someone buying rental property today to provide a source of income in retirement 30-40 years from now has a different set of metrics to screen a potential purchase than someone who needs cashflow today to replace their current W-2 income. 

Wife's property management duties also included inspecting units, preparing units for rental, advertising vacant units, screening potential tenants, showing the units and processing rental applications.Wife produced two spreadsheets detailing her rental management activities.

Or maybe find a PM company who will help you screen and place tenants for a fee and you manage once they are living there (this is a hybrid approach).