A general rule of thumb I’ve heard is your mortgage should not exceed 3x your gross annual salary. So based on your above situation, a proposed mortgage of $375k + your $17k for DP equals a purchase price of $392k (less closing costs you’d have to pay). Hopefully you have at least another $10-15k in savings that you’re not allocating as your DP. You’ll also be limited by the FHA front and back-end debt-to-income ratios, which will take into consideration your auto loan.
In addition to job stability, a HUGE factor that people in our age group don’t consider is having children and the impact on your income/expenses. If you’re not planning on having kids ever, then the above math might make sense (assuming you feel we’re at the bottom of the housing market, which I don’t). If you are planning on having kids, you must consider one income going away or a significant monthly expense for full-time daycare. This will change the math dramatically.