I'd set up a Roth IRA at the very least. Throw $6k in there and invest in some index funds. Get your feet wet investing and get used to saving for retirement. The market is down a decent amount now, so there is likely more upside than downside at this point. Of course, anything could happen. Be prepared for the value to go down further. But better now than the beginning of this year. If you decide you need this money for the house downpayment, you can withdraw the principal from a Roth IRA. For a first time homebuyer, I think you can even withdraw some earnings too without penalty. I'd recommend keeping it in the Roth if at all possible though.
Do you have a 401k? Does your employer match it? This should actually be priority #1 if there is a match. This is free money. Either way, I'd set aside at least 5-10% to start from every paycheck for retirement. If you don't have a 401k or HSA and put the $6k in the Roth IRA already, open a regular brokerage account. The key is getting used to saving for retirement and investing regularly. You're doing a great job saving, but it's time to put some of that money to work! Get used to seeing the volatility in the stock market. Don't panic, just stay invested.
After that, it's up to you to decide which goal is more important to you. How much does the average house cost in the area where you want to live? How does that compare to rents? Does it really make sense to buy? If so, I wouldn't put any more than 20% down if you have no retirement savings.
Unless you are sure you
really want to have your own house in 2 years, I'd probably invest 1/2 of your savings in index funds and keep 1/2 a bit more liquid. There is a risk your investments will be down in 2 years since that's a pretty short time frame. But it could grow as well and help you reach your goal faster. Only you can decide if it's worth that risk.
Also consider investing $10k in I bonds which are currently paying 9.62%. The rate changes every 6 months based on inflation. You'd have to buy before the end of the month to get this rate for the next 6 months. The money is locked in for 1 year. So if you want to buy a house before then, it wouldn't make sense. But since you said your timeframe was 1-2 years, it seems like this fits. If you buy this month, I believe you'd have access to the funds on Nov 1, 2023. You'd lose the last 3 months interest if you redeem before 5 years. But with the high rate for I bonds now, this will still be much better than a savings account over the same timeframe.
The Treasury Direct site is where you need to buy I bonds if you're interested:
https://treasurydirect.gov/savings-bonds/i-bonds/i-bonds-interest-rates/There's a thread here about I bonds that might have some more useful info as well:
https://forum.mrmoneymustache.com/welcome-to-the-forum/series-i-savings-bonds-for-emergency-fund-3-54-interest-rate/
