Once you have three to six months pay stubs, as a co-signer, it shouldn't be that big of a deal. So if you have a new job opportunity that you want better, you might want to take it and then buy a home in a few months.
Also look at your credit (FICO) score and spend time inching that upwards. Every set of points that FICO goes up gives you a better loan rate.
Most lenders have some steps you can take -- for instance, declining an offer of a free credit card can give you 25 points. So, look at everything you can do to get FICO high. Both you and your partner should seek to increase the FICO as high as possible before the loan is "locked," because the higher the FICO (coupled with the other factors) the lower the loan rate.
On income, the big information is ratio of income to debt.
A good job is actually very precious. I wouldn't stress on the loan approval unless you want to buy a house within the next two to four weeks. Then, buy the home, and then take a new job. But new jobs in good fields where you've been super eager are very special. The fact that you are one of two incomes and the other income is steady (if that is the case) should be a good buffer for you. Do get with a lender but don't let a loan officer make your job and career choices for you! Princeton Capitol has a really good system for approvals, it's also got excellent loan officers. Wells Fargo and Bank of America are among the most conservative as far as the "rules" around who can obtain a loan. So within lending institutions, you're going to see different responses and different sets of standards. They are not all equal.
Hope this helps!