Not only do they generally accept plastic (except AmEx), but also they sometimes get rather annoyed when you use your chip-and-pin card, as most customers tend to use touch-to-pay, which makes for a faster transaction.
On my recent two-week trip to Moscow, I had to use cash a total of maybe 5 times, two of them in a public restroom, and three to get local commuter train tickets (the machine temporarily didn't accept cards). Plus, all tips are always cash (the cheques don't have an extra entry line for tips).
As far as cash goes - I'd take out 4,900 rubles for starters - that should be enough to cover ongoing public transport expenses and a nice meal at a restaurant - and then see how it goes.