I agree that you should definitely at least contribute enough to your 401k to get your match from your company.
In most HCOL areas, they have great transportation systems that make it easy to get by without a car, but if you really think you need one, you can start saving up for one. There are online savings accounts that give you pretty good interest, around .8% is pretty common, I would start one of these if you want to start saving for a car, It shouldn't take long to save up for something like a 5-10 year old Toyota Corolla or Honda Fit.
It sounds like it's probably not the best time for you to buy a house, I'd way for everything to settle, then do the math
http://jlcollinsnh.com/2012/02/23/rent-v-owning-your-home-opportunity-cost-and-running-some-numbers/and decide if you really want to buy a house. I agree you probably want to live there for a minimum of 7 years to not lose money on closing costs etc.
If you do decide to buy a house, I would recommend opening up a Vanguard account to start your saving, keeping the money in a bond fund(I like the vanguard long term bond index VBLTX). Once you have enough to put 20% down on a house you can go find a good one and buy it. I'm not an expert on buying houses, but I hear the good deals are gone within a day, so when you start looking you want to check everyday, and when you see something you like, look at it THAT DAY, and if you are SURE you want it, then make an offer. But like I said I'm no expert, so talk to someone who is more real estate savvy
After taking care of these things, I would start maxing your 401k and traditional IRA and if you are able to save more than this, put the rest into a vanguard trade account. I would put this money into index funds, either Total Stock market index funds or S&P 500 index funds, preferrably through vanguard but that might not be available in your 401k
Rather than start your babies a college fund, you should just save as much money as you can in your own accounts, and when the time comes, you can help them if it works out. If you start saving 60% of your income now, in 16 years when they go to college you will have more than enough to help them out.
Good Luck!