Without knowing your interest rates, it's hard to say exactly how to handle things.
Credit card is probably the worst rate, kill that first and as fast as you can (stop throwing extra at lower-interest debt if you are doing that). Then hit the car loans (if >4% or so).
Is there a particular reason you want to buy a house? Buying a house (contrary to what so many say) is NOT ALWAYS the smartest financial move. You are NOT "throwing money away" on rent. In plenty of areas, buying a house is downright stupid. I did buy a house, and a second house (renting out the first), but I had/have a plan and lifestyle choices (pets) that give me reasons to do it. I'm not trying to discourage you, just make the choice a deliberate one if you do end up buying.
If your student loan interest rate is above about 4%, I would definitely pay it off before saving for a house. I would definitely pay off everything else before saving for a house. If your student loan interest rate is crazy low, I'd hold it, pay the minimums, and save/invest the difference.
Do not buy a house without some extra cash reserves. If your roof leaks a month in, be able to swallow that bill. If you need to spend $5,000 to fix a sewer line a month after that, be able to swallow that. Maintaining/repairing a house is not free. Your mortgage payment is just the beginning of house expenses.
With that kind of income (and increasing in two years), you should be in great shape once you get everything dialed in. My girlfriend and I have a household income of about half what you do, and at 25/23 we're on our second house (first rented out and almost paid-off), have two (not financed) cars, and are living a pretty damn good life, if I do say so myself. Student loans and HCOL will be your main roadblocks, but you've definitely got the income to take care of that.