I think you're definitely on the right track. My advice would be:
1) Yep, step one is to fund a rainy day fund. If you don't have a savings account at your current bank set one up to keep the account 'separate'. I wouldn't mess with money market funds given the low rates of return, no FDIC insurance, but that's just me. This may be 3 months living expenses, may be 6 months. Depends on your comfort level, risk tolerance, etc
2) 100% agree on Vanguard funds. I don't put my stock market investments anywhere else and you shouldn't. Continue to read about them. I'd suggest the Gone Fishin' Portfolio book, and the blog by JL Collins as a start.
3) As far as allocating your excess cash flow after the emergency fund is set up, maybe save 1/2 of your excess each month into a New House Fund and the other half in Vanguard. Keep in mind you'll need to save up $3K per Vanguard fund to get started unless you do ETF (and I wouldn't). Start with the Total Stock Market Index Fund (VTSAX).
4) Keep in mind, these Vanguard investments are liquid, so you can draw upon it in cases of emergencies. In other words, this supplements your rainy day fund. But I'd suggest you plan on NEVER selling them. At least for a long time. Jumping in and out of the market will kill you. That's why I recommend building up the house fund separately, rather than liquidating Vanguard funds when you are ready to buy.
5) Stay away from buying individual stocks for a long time. If you ever do, make sure it's 'play' money, do a LOT of research and focus on dividend paying stocks. There are a lot of FI blogs about dividend stocks, but this requires a lot of research. Start with Vanguard.
6) Consider residential real estate investing at some point, depending on where you live
Jason