Well, the easy rout would be to start calling ads on Crags list and before paying to fill out an application just be upfront with the owner and ask him/her if you can rent there.There are people who will rent to you, but most will run a background check on you.Some will want first, last and a security, some only first and security.If you are under-employed and have a co-signer, its not a lot different than a college rental.I'd say just start calling ads in Craig's list on after another and if someone say OK, and offers to let you apply for a fee (to run a personal background check) then make it happen.https://www.youtube.com/watch?

I’m not into renting with background issues.

I had no background in any construction work, but youtube became my best friend. 

That being said, I have learned a significant amount of knowledge since joining this site and really appreciate the plethora of different views and backgrounds. 

What would be the best way to start investing in real estate with this public record on my background? 

But if you let me know the ones you're looking into, message me and I'll be happy to share any experience or background info I may have.

The background is that my current tenants, doing some troubles with rent payment, their lease ends on 31 July, and they bought a house.

I posted my rental online with 2 open house dates on Saturday and Tuesday. should I take all applications from those 2 days run background checks and pick the best Tenant.

@Paul Winka - The pilot analogy is a great one, and it's interesting to hear your background.

I can do a quick free background check on the person, and if no major issues we send them the code for a self-tour.