Have you thought deeply about the reason why you want a house so soon? An article for your consideration:
http://jlcollinsnh.com/2013/05/29/why-your-house-is-a-terrible-investment/I would suggest really thinking through why you want a house so badly, so soon. A house is not an investment, it is a consumable that you buy to store your stuff and sleep in. If you are interested in FIRE, or FI, it really sucks all your momentum to tie up significant assets early in your accumulation phase into an asset that basically only tracks with inflation.
Instead, I suggest you focus on saving in solid investment vehicles as early as possible. The Rule of 72 states that investments in the stock market will DOUBLE every 10 years even if you don't add a single additional penny. The earlier you start, the more doublings you get. So if, by 30, you save $200k and stop saving completely, at 40 you will have $400k, and 50 you will have $800k, and at 60 you will have $1.6 million. BUT, if you buy a house and therefore delay accumulating stocks, and only accumulate ~$100k by 30--a mere $100k difference. But, that one move leaves you with $800k LESS that you would have if you had focused on stocks first.
That is just an example. But basically, time in the market is most important. Because you say you want to take advantage of the decade of your 20s, that means you should buckle down, minimize your expenses (your 20s are generally the cheapest, most flexible decade of your life, so take advantage!), and invest as much as you can. Later, when you reach a solid number, you can scale back and then focus on spending/saving for other things like a house. But take care of your retirement first!
For reference, I am only 3 years older than you. Someone here on this forum gave me this same advice a few years ago when I was eager to save for a house, and DH and I are very, very glad we took it. We are planning on renting for at least another 5-7 years, and shoveling money at our investments. Then once we hit 30, we can scale back working, have kids and spend a lot of time with them, and just cover bills while maybe saving for a house, while our investments grow in the background. Then one day, we will wake up with FI money, and maybe we will have a house by then, maybe not. But saving this aggressively during our 20s in stocks specifically is setting us up for a much more relaxed life, because we get the luxury of an entire extra doubling that most people even on this forum didn't.
Anyway, your 20s are a time to maximize income (your incomes look low for a MCOL area) and minimizing expenses, and investing in the stock market as aggressively and early as possible.
Unless you have a very strong need for owning a house, I would avoid it like the plague. Unless you are planning on house-hacking, houses carry a LOT of costs and lost opportunity (downpayment goes into the static house instead of growing your investment portfolio and working for you), and renting is often not as bad a deal as american culture likes to say. I'd poke around and see if there were better rental deals out there, but in your position I really would consider holding off buying until your 30s.