I have not read all of the other posts, so forgive me if someone else has mentioned already. 

You don't mention potential income, either gross or net, so we've got to assume it's not real great.

As has been mentioned already, if you go at this from the investing side the banks will look at the loan much more from how good is the investment rather than just you.

As mentioned above, it might be better to wait until all the work is done and title is clear.

You mentioned having two jobs so perhaps that could be feasible for you.

As another poster mentioned you may have to offer on more properties but you won’t overpay and you won’t miss out because your offer had expired.

Or, as you mentioned, if you already have one that you'd like to use, you can ask an attorney to do "doc review" for you. 

It is possible that the 'no comment' response is because of no experience for the property management company, but at the same time is it a red flag you want to rule out before taking these tenants on.Lots of good suggestions mentioned here- checking out their car, their current apartment, etc.Good luck!

Was mentioning, very few people have enough money to self-insure liability.

Not to mention some of these countries have unemployment levels as high as 30%, so you could rent to someone who has never had a job, may not speak English and can't drive a car.