I'd want to know why their credit score is below 600. Poor choices 5 years ago and nothing negative since, defaulted student loans, or current unpaid credit cards and utilities. Makes a big difference.
A credit score is not the whole story. Some people have low scores because they pay cash for everything. Some are due to a divorce that happened three years ago. Some are due to medical collections due to lack of insurance.
This is exactly why I use the "whole person" concept. Based on what you've written, I would probably approve them for a $700 apartment. If they were higher risk, I would charge them a larger deposit.
In order to protect yourself from fair housing violations, you need to have a written list of criteria that people must meet in order for you to rent to them. That criteria can be anything, as long as it doesn't violate fair housing laws.
The reason I bring this up is it seems that you don't have this, and it's important that you have a written procedure that you follow every time. In my area there are lawyers and law students that call and walk through properties asking all kinds of questions in an effort to get a landlord to slip up so that they can either prosecute or hit you with a hefty fine.
Best of luck!
My decision would be no for multiple reasons determined by my official and personal reasons.
I do not rent to anyone relocating as they will often choose to move to a temporary apartment with the intent of then seeking a more ideal unit to move to. I also do not rent to anyone unemployed. New jobs are not secure.
Credit score does not meet my minimum requirement. If your screening standards have a set minimum this can not be negotiable otherwise you have no standards. Offering mom as a co-signer is a serious red flag as it indicates there is no likely hood of them increasing their credit score. This indicates a lack of financial planning. You could check for the reasons as to why there is a low score but the likely hood is you will find a poor payment history. Expect on going excuses for late rent payments. I do not waste my time trying to make applicant work.
I also do not rent to police officers.
@Thomas S. - just wondering why you don't rent to police officers?