This is an often asked question, if you do a search on the forums you'll see this question a lot.
Start by reading the MMM blog:
http://www.mrmoneymustache.com/2012/03/19/top-10-cars-for-smart-people/It is a couple years old, but a lot of the cars and advice will still hold true. Just because you're planning to have a kid doesn't mean you need to start thinking about a big SUV. All car seats have to meet the same standards, after that you buy them based on size and extras.
When I bought my 3 year old hatchback I bought something I liked, with good mileage, and I would want it for at least 10 years. I also knew that I would have 1-3 kids before that 10 years, so I made sure I could fit 3 car seats in the back. I paid cash for it, more than I probably should have ($13k), but overall I really like my car.
As far as financing it or not that really depends on you. When I bought my dad a car, I had the cash to buy it, but ended up financing it for 1.9% because I knew I was going to get a mortgage eventually, and my credit was around 650. Now my credit is around 720, we bought a house (a year after my dad's car), so I'm planning to pay off that car next year, because I hate the idea of owing a bank or anyone money.
you should figure out how the car will be driven, then look for something with good gas mileage that fits your budget. As long as you have a back seat with seatbelts and a trunk you have room for kids and their stuff. With a $10k budget there are a lot of great options available to you.