I will also note that I am currently single, and I understand that having a working spouse/partner would be an extra income source. But if I am still single when I want to buy, I want to be able to buy on my own.

Adding more debt can lower your credit score as it increases your debt utilization ratio, which influences your score.

It depends on the timing of your “down the road”, if it’s within 6-9 months, I’d probably hold off on the new car to have more flexibility.

^^ This. DH did just that when we were house-hunting, he drove his old beater until the mortgage was signed and then ran out and bought his new vehicle immediately afterwards.

"Adding more debt can lower your credit score as it increases your debt utilization ratio, which influences your score." I find it odd that less debt can also lower your score. My score when down I paid off a HELOC, then down again when I sold my house and bought my (downsized) house for cash. I have no debt except credit cards, which I pay off each month, and my score is lower than when I had a mortgage. I don't really care since I don't intend to finance anything, but I've realized that my previously fairly high score (820s) wasn't really indicative of my finances. And I've stopped caring when I get alerts that my score went down, which has happened when I pay off a large cc bill.

would have between $15K and $20K in savings left over after the down payment on the house if I buy the car.

Do you have any kind of emergency savings fund on top of that or is $15k - $20k your complete and total savings?

I would not put yourself in the position of being a homeowner and having that be your total savings. There are many unanticipated expenses, things that break, especially after a home purchase. If you have to spend a good chunk of your savings on those remedies then you have no cushion for life emergencies like losing a job or having an illness.

Your best bet is to talk to a mortgage broker and lenders. When I bought my first home my credit union offered a better deal than I could get with an FHA loan through a broker or lender or a conventional loan. You have to do your research and compare all of your options.

If you don't have to buy a new car, I would not buy one now. I would, however, start paying the payments to myself. Open an account and put that money that you would be spending on a car payment and increased insurance payments away each month. Put it in an account that is going to give you a safe, but decent ROI. You should also pay yourself the difference between rent and your mortgage. Put that money away toward your home purchase. If you can really afford that 55% DTI ratio it will not be a hardship to put that money into savings.

Every penny you can pay toward your home or toward a new car is that much less you need to borrow and that much less interest you will pay in the long run.

Other than the very first car I purchased I have never had to take a loan to buy a car. I just kept making the payments to myself after the car was paid off and always had enough to buy another car when my car was shot.

"^^^ What kind of creditors do banks want? Don't they want creditors who take on debt and pay the interest on it?" Yes, exactly, which is probably why my credit score went down when I no longer had debt, as I no longer had proof that I can and will pay off debt. My comment above was replying to the assertion that "adding more debt can lower your credit score" which may be true in most cases, but in my case, decreasing or eliminating debt is what lowered my credit score.

You are right @chicagoansI have always had terrible credit because I have very little debt. I never carry a credit card balance, never had loans. It doesn't give you a good credit score.

I totally agree it’s nuts Chicagoans!
Your debt utilization ratio which is a part of your credit score is not a very accurate reflection of your financial situation . It almost seems as if the available credit number reflects the absolute max and individual could carry, which is not necessarily the case. As pointed out here, not everyone likes to use credit, or have endless open accounts.
It has no connection to your actual income or assets-so it seems - a benchmark of dubious usefulness.
I allowed a credit card with a very large limit to be closed as it was “dormant“ according to the merchant. I either had to make a purchase by a certain date or the account would be closed. Didn’t care to make a purchase, but the outcome after I let the account lapse was that my credit score declined!
Bottom line- you can’t beat them- better to ignore it as much as possible and live within your means.