I've got a couple calves just over that size. Raised on my nurse cow, weaned and started graining them between 250 and 310lbs or so - they're all pushing 400lbs now. I try to grain mine at about 2% of their body weight, sometimes less, depends how much weight I'm trying to put on them. Mine don't always grow right on just grass at that age; tend to get a little potbellied.
I start 'em on free choice when I wean, but they generally don't eat much more than a pound or two per head per day. At that size and weight, that's about 1% of their body weight.
As to grain - I've been putting mine on a mix of Purina Growena, barley, corn, and cottonseed - they've been growing really well on that. Right now my grain bill runs about $3/hd/wk. Might be a touch less. Reasonable.