I've started as a lender in 1998. Your car payment will reduce your home buying capacity. If a lender allows a debt ratio of 45% and you make $5,000 per month, your total allowable debt payments would be $2250 per month. If $500 of this is already going to a car payment, your maximum house payment will now be $1750. The actual ratio will be different, this is just an example.
Buying your first home is a major step and it sounds like you are doing a great job with your job & credit. When you meet with a lender they can look over the specifics of your situation and advise you based on more information. Until then, I would make your car payment on time and save all you can. You can always pre-pay the car if you want to go lower down payment.
It seems that you are very care about your credit with paid student loans and no other debt but the car loan. If you have sufficient income in comparsion to the debt ratio, then should no problem in getting a mortgage. Please let me if I can be of further help. I will be gladly to work with you.
Having a good mix of credit will help keep your credit score high.
Also as a first time homebuyer, you may qualify for the new federal mortgage tax credit. There are income limits to it and it is different than the old $8000 tax credit.
Email me if you want additional information. Many of my clients use this tax credit to pay for their mortgage insurance premium.
All the best,