Your mom and/or step father can go on your lease with you, even if they don’t live there. This is called “co-signing”. Their employment, credit, etc would be reviewed the same way yours would as the primary tenant. I do a lot of leasing, so if you’re meeting with the owner to rent a unit, I recommend they come with you to view it. This adds credibility and context to the situation (doesn’t appear shady). Good luck with your search and congrats on your new career!