Is your wife's income low enough that you qualify for a Roth IRA? If so, I'd start putting $400 per month in a Roth. If not, you may want to do a traditional IRA-->backdoor Roth. That amount will pretty much max you out for the year. When eligible for 401k employer match, contribute enough to get the match. As for your $10k savings, you may want to keep about half of that (or all) around for an emergency fund. It it's "extra" right now, throw it at your loans, maybe pay off a small one if you can. After that, if you can pay $1000 extra per pay period, you'll start seeing the progress in no time!
Personally, I've been paying my loans highest interest first, but I don't have private loans. If the terms aren't too onerous, I'd start by paying the minimum on those, with a plan to start paying more if interest rates go up. 3.8% is a lot lower than 6.8%, but federal loans have more consumer protections, from what I've read around the web.
As far as the house down payment saving goes, I'd wait until you've paid at least half of your student loans, and then reassess the situation.
What sort of portfolio are you looking at for retirement savings? I know the stock market is volatile, but you're young and have time to ride out the swings. A target retirement fund (Retirement 2050 or 2055) with Vanguard (low expense ratio) is a good place to start if you want to keep it simple for now. Whatever you do, remember that index funds outperform the majority of actively managed funds.
Whew, that was long! Hope it helps, and good luck on hitting those loans with all you've got! Keep your expenses low and you can make a major dent quickly.