Verifiable income can come in various forms. An apartment complex will typically will look at your employment history. They like to see that you have six months to a year of employment history. They also want to see that you earn three times the rent. So if you're looking to spend $700 on an apartment, they want to see that you earn at least $2100 a month in gross monthly income, which is your pay before taxes are taken out.
There are some apartment complexes that require an income of three times the rent to qualify. There are some affordable housing complexes that qualify based on 2.5 times the monthly rent and there are some management companies around town that will do two times the rent. But the norm is three times the rent to qualify for an apartment
As far as what proof of income apartments will need, a paystub is usually the standard, but bank statements would be an option if you are relocating to Austin and are still looking for a job. In that case, an apartment manager wants to see that you have the amount of the rent times the lease term. In other words, if you are leasing an apartment that is $700 per month for a twelve month lease, they'd want to see $8400 in your bank account.
If you are just starting a new job, apartment complexes won't hold that against you. They will just ask you for a letter of hire on company letterhead stating when you plan to start your job and how much income they anticipate that you will be making.
If you are a student or do not have the required income, you can use a a co-signer. A co-signer is a person that is willing to vouch for you and can ultimately be held liable if you can't pay rent. The apartment complex can fax a co-signer application to your designated person, usually a parent. The co-signer doesn't have to live in Austin or even in Texas to qualify. The co-signer just fills out the co-signer application and returns it and the complex will use the co-signers income as verification. The co-signer does typically need to make more than three times the monthly rent.
Some complexes do not put as much emphasis on the income verification. They will look at credit, criminal history and they will use 401k's or gifts as proof you can afford the apartment. Sometimes apartments will even allow financial aid if an applicant is a student, as long as it shows enough income to suffice for the entire semester.
If you have any questions about income verification, be sure to contact a qualified apartment locator.