More the better obviously, and if you can survive the loss of bank savings rate (mine is 7.5% for the first $750, but something like 3.25% for amounts more than that).

One way to accumulate the money - every night, I come home with loose change and dollars in my pocket. I put the $1s and sometimes the $5s and $10s in a drawer. Its done, and the way things work my wife draws from it as necessary for the kids or pizza, and so do I, but it does accumulate over time. $1 bills seem to be the new quarter, you can accumulate them and not miss them if you set them aside. Every now and then I also pocket a $20 this way, and as a result have $750 set aside in small bills, over $100 in ones, and a roll of quarters in each vehicle. I also have $100 in small bills set aside in my car, though I expect that to get stolen during a breakin, but it has been a good idea at least twice to have ready cash in the car. Just accumulate it as you go, as you can. For a long while I stopped at $500, then recently upped it to $750 cash.