Alright... so. One thing at a time.
Owning a house and renting it for mortgage + 300 sounds like a pretty good deal, but it has some pretty big downsides: since you're two states away and don't plan on going back, what happens if shit happens? Will you have to go deal with it? If you want to be a landlord, you should understand the 1% and 50% rules (suggestions, but good ones) to figure out if your property is a decent investment. Part of that is figuring out where the 300 goes - taxes? maintenance and repairs? in your pocket? etc.
Living together with your fiance would mean the two of you can cut your housing cost in half, give or take. Quite a nice thing.
401k and 403b and IRAs are excellent in that they are tax advantaged. You together earn 95-100k. If you max out the 401k and 403b, that's $35000 pre-tax. Add an IRA to that for each of you and that's another $11000 pre-tax. (Of course you have to ask: when you draw on this money, will you be earning more or less? If more, than go roth. Probably.) If you did this, you would put away $46k and be left with about the same amount...
So now there are two questions: First, can you live on $46k for the two of you? Second, remember that you can't draw on the money for a long time (well, you can take out your contributions into your roth ira penalty-free, but that's a different story.) Will you need money sooner? If so, you might consider roth IRAs instead, or you might consider paying a bit more taxes now and putting the money into a taxable investment account.
Now, the cash - that's a ton of cash. What's six months or a year's worth of expenses for you? Can you comfortably put some of that cash away for now? You can throw it into an IRA right now. You can also increase your 401k/403b contributions to their max - and given that there's only half a year left, you might find that to reduce your remaining paycheck too much, and use the cash to make up the "shortfall" in the paycheck. You can also open up a taxable account.
As far as where and how to invest, there are a couple points to look out for. One: risk tolerance. I'm young and single and put 100% into index funds (stocks). Maybe you're less tolerant of risk and want to put some into cash/bonds. That's up to you to research. The main thing I'd recommend, however, is to understand this: First, index funds track the market, and do well when everyone else does well, and don't lose money making poor choices like an actively managed fund might. Second, very low cost funds are generally better, and those are index funds. Everyone here likes Vanguard but the big guys from other firms offer them too - schwab, fidelity, whomever.
If I were you: Keep renting the home to your friends until they move, then sell it - or sell it now. Buy a new home for you and your fiance and move in, if it's cheaper than renting. Max out pre-tax savings contributions. Invest in vanguard index funds (total market - vtsmx or the equivalent ETF.)
Required reading:
http://jlcollinsnh.com/stock-series/