First: get a copy of your credit report and FICO score.  The higher the score, the less hassle you'll face.  If you have a lower score (FICO>680), you'll have problems and have to prove income.  

Second: If you don't have a bank account, GET ONE at a local credit union.  Start depositing 3000-4000 a month into it.  You'll have to depend on bank balances to prove income.  Better have six months or more of a track history.  

Third: Looking at your information, there's not a lot of a history showing.  You'll have to build a self-employment profile, and most leasing companies are going to ask for 1-2 years of 1040 + Schedule C as well as 6 months bank statements to prove a) you can afford rent; b) you file and pay taxes and are an honest citizen.  

Finally:  If the income does not verify, or you don't have a solid history, you'll need to find an individual-owned property, or talk to a Realtor and find out what you can do without Verifiable POI.  

Bad thing about Vegas is the sheer number of management company run properties out there.  Don't even think about looking for someone to create paystubs or other documents so you can get a loan.  It's called FRAUD.  You defraud a bank or worse, a credit union, you are looking at Federal violations..

let me know you know if you have questions.