An emergency fund is there to buy you time to figure out what to do / how to pay for whatever unexpected life event happened. The emergency fund amount is a personal preference, and also depends on what you consider an "emergency". In my case, the only reason we'd touch our emergency fund is for a job loss or catastrophic medical issue. We budget for car / house repairs and other pricey recurring expenses. My wife is a SAHM, so we prefer to have 6+ months liquid (savings account, CDs) in case I lose my job so we can keep life as "normal" as possible for the kids while I find a new job. I don't want to put it in the market and risk it losing tons of value, because a market crash is likely to coincide with a layoff at my company. I know I am forgoing a lot of potential market returns, but we've got a pretty solid amount in our retirement accounts, so we're willing to sacrifice some return for the certainty of the amount available on any given day. When we were DINKs, our EF was only about 3 months of take home, because we were young, invincible, and only responsible for ourselves.
I'd start with 6 months in the EF. I know most folks here are against treating "found money" any differently than any other dollar you have, but in this case, I think you should. You essentially get an instant, pain-free emergency fund. I know it's not sexy, but just set it and forget it. Once you settle into married life, buy the house and all of the associated stuff you need when you own a house, and get a handle on what your new level of spending will be, you can reduce the amount to whatever you're comfortable with. For me, it would be easier to go that way than only have 3 months in the bank and then realizing you really want 6 months in there and having to fund it. Also, as your income grows, today's 6 months in the EF might naturally reduce itself to 3 months anyway.
Given your level of income, I'd contribute enough to your 401ks to get the match, budget to completely fill both of your ROTHs every year, and contribute anything you can beyond that to your 401k (assuming the fund choices are good). There are plenty of threads on here on getting started with retirement saving, so read and do what's best for you.