Most people solve the size question first and then park the money wherever it already was. That's usually the checking account, sitting under the same balance you look at every time you buy gas. Money you see forty times a month gets spent.
The account you want does two things. It pays you something while it sits, and it takes a day or two to reach. Not a week. A day or two. Enough friction that a slow Saturday afternoon doesn't turn into a new TV, and not so much that a tow truck driver has to wait on you.
A high-yield savings account at an online bank hits both. The transfer back to checking usually takes one to three business days, the rate moves with the Fed, and the deposit is federally insured up to the limits like any other bank account. A money market account at a credit union does close to the same thing. If your credit union pays a tenth of a percent, that's your answer about whether to keep it there.
Where this goes wrong is reaching for yield. A twelve-month CD pays more, and it also charges you months of interest if you break it early, which is the exact moment you'd need it. Same problem with a brokerage account: the money's available, but you might be selling on the worst day of the year to cover a transmission. Emergency money doesn't have a return target. It has a job.
Split it if the number is large. A household carrying six months of expenses doesn't need all six months one transfer away. Keep one month in savings where you can get it today, and put the rest somewhere paying more, like a Treasury money market fund or a short CD ladder where one rung matures every few months. The first month buys time and the rest buys yield.
Name the account. Most banks let you nickname it, and "Emergency" on the screen does more than you'd think when you're deciding whether to move $400 out of it for concert tickets. A separate account at a different bank than your checking works even better, because it doesn't show up in the app you open every day.
One thing people skip: make sure the transfer link between the two banks already exists and has been tested. Setting up an ACH connection the day the water heater floods the basement means micro-deposits, two business days of verification, and a phone call. Move ten dollars over and back when you open the account, and the plumbing is ready before you need it.