The amount that's best for you, and the method that's best for you, will vary based on your situation. Things to consider:
1. Your age and your health -- are your healthcare costs high, or do you have reason to believe they could become high soon? is it likely that your health will interfere with your ability to work?
2. Your responsibilities -- spouse? kids? mortgage? debt leveraged to the hilt?
3. Your income sources -- how reliable is your line of work, especially in a recession? if you lose your job, do you have other income coming in?
4. Your other assets -- if you didn't have income coming in, what other assets could you access besides your EF?
5. Your risk tolerance -- what's gonna keep you from panicking?
For me -- I'm healthy and relatively young, have no dependents, and have relatively little debt and no mortgage. That means that I can keep a smaller amount for my EF than I might otherwise, because I don't have to worry about providing for children and a spouse while dealing with side effects from lupus and paying a mortgage. I personally keep ~5 months of spending in my EF, which is much less than I'd be keeping if I had kids.
On the other hand, my job (although well-paid) is in a sector of the economy that got hit really hard by the Great Recession. I'm also early on my journey to FI and just plain don't have a lot of assets. I therefore don't keep my EF in an investment vehicle, because job loss for me would be most likely during a downturn, and I don't have a ton to draw on outside the EF. If I need that money to live on, then I really need to be assured that it will be there!
I, like HamsterStache, keep mine in a Capital One 360 MMA; 2% is below inflation, but it's not the worst. You may find other savings accounts or money market accounts that get better interest rates. My personal view here is that my EF has nothing to do with investment, or with growth; it's self-insurance against job loss and medical emergency. It is for my safety, not my progress forward.
Depending on your needs, you may also be interested in a CD ladder or I-bond ladder. I personally was pretty meh about this, because I wasn't finding CDs that were short-term enough (6 months or less) with the amounts I wanted ($2500 or less) with a good enough rate (i.e. better than my 2% MMA). I also don't like the amount of management I'd have to do with that, frankly.