As long as it goes to checking, that's alright! You'd be able to use your last two or three months of bank statements as proof of income.
Yes, you will still get good rates. What kind of credit does your cosigner have? It'd be ideal if we knew their FICO score haha...or even a free FAKO score from like creditkarma would help to an extent. BTW if cosigner has a Discover, barclays, or Capital One card that they are the primary holder of, they can get a free FICO from the card issuer (in their online banking / statement for Discover). Even if they have bad credit, your good credit will certainly be considered. Some financial institutions use only the primary applicant's FICO, others use both, but obviously having a good one helps even if it's only 1 applicant.
Also when you go to the dealer this time, you can still try to get it financed by yourself. Don't even mention the co-signer at first imo. If they can't get you financed or give you a high APR, then bring in the cosigner, etc...
But more importantly, please think this over. You're proposing buying a lot of car for your income. IMO you might get in over your head. Do you really need a 26k car? Have you budgeted for everything? And what about rent? Remember you're going to have the car loan for 5+ years, you may not want to live with your family when you're 23 or older. 