Hey Justin! This is one of the most asked questions I get from my newer investors who are holding rentals. This is a tough one. So i've been an investor and real estate agent for a while and here is what I've seen work.
1. When screening, you need to have the same process across the board. I don't look at credit scores that much because they are easily changeable (like can be made to look a lot better then they should be lol). I do make sure we have 3xs the rent income or 1 years rent in savings. Also we heavily look at residential and employment history. If you have a lot of job hoping then there will be disruptions in their pay which means disruptions in their rent payments to you (more times then not). You are looking for more character references then anything. Never and I mean NEVER trust a landlord reference. Some of my best landlord referenced tenants have been my biggest nightmares. Either they lie about the contact info and have a friend talk them up or the landlord is just so desperate to get rid of the tenant they say whatever they need to do get them out. Really look at their employment and rental history and the rest should fall into place
2. You need to prequalify them a little before showing. We have 4 full time agents on staff and even with that we are often booked. The worst thing you want to do is show a place, they love it, and then you find out they can't move in for 4 months or they want to move in immediately and you have a tenant in there until the middle of summer. Make sure you check move in date, pets, and give a general overview of requirements for your application to make sure they meet it. They could lie but more often then not tenants will let you know upfront about any potential issue for the app.
3. Co-signers can be included in the eviction but they need to live in the same state. At least where I am in Pittsburgh, if the co-signer lives out of state i either cannot do anything or do very little to hold them to the eviction and repayment. A very well qualified co-signer will not want the hit on their credit or the potential garnishment of wages if something goes wrong
4. This has been the biggest thing we have been struggling with. You do not want to loose momentum in the market but you also don't want to waste your or anyone else's time. We give the approved applicant 48 hours to sign the lease and pay deposit or we put it back on the market until they do. During that 48 hour window we tell all other applicants we are scheduling for 48 hours or more past to allow time for the applicant to sign and if they do, we will call you back to cancel. This also lets them know if they end up being the applicant that has the time limit put on them, you aren't joking around. You will keep scheduling.
5. Zillow and facebook market place are still the best.
Hope that helps a little. If you ever need anything feel free to reach out!