I'd definitely recommend putting a large piece of the extra dough (and most if not all of your emergency stache) in Vanguard index funds. I've spent years reading investing books and such, and quite simply that's the best way to go in my opinion. Fantastic company, extremely low expense ratios, everything is online (direct debit for your investments), and you can get your money debited to your bank account in a day or two if the need arises.
Now the next question becomes of course, which funds?
My best advice would be to read the Gone Fishin' Portfolio by Alexander Green. He's a former Wall Street insider who explains why you should avoid professional advisors and manage your investments yourself, why index funds (and Vanguard) are the way to go, and then he lays out a portfolio allocation to set and leave (ie go fishing afterwards). It's a very good starting point for your investing, and you don't have to invest in all funds right away. Start with one or two and add as you can. You can also get the allocations on the website I believe, but I'd check the book out at the library and read it for your education.
Finally as a sidenote, Alexander Green has some other great books that are very Mustachian in nature, like Beyond Wealth. Not an investing book, rather a series or articles speaking towards the better things in life (other than money).