This is the kind of signing Manchester United used to make under Ferguson. Think Rio, Carrick, Rooney etc. Big money England internationals, pre-prime age. As an Arsenal fan I always used to think "bloody hell that's a lot of money" but all of them went on to become key players in multiple trophy winning teams.
Rice is expensive because he's a lock. He's a cracking player, well established as one of England's best midfielders and proven in the Premier League. We will get 5-7 good years out of him at a minimum. He will strengthen a team that just finished 2nd with its highest goals tally since the Premier League began. It's OK for us to be excited.
To be honest it is an insane role reversal to be watching United fans talking about how Arsenal are spending too much on a player. Too much? I've lived through a lot of Marouane Chamakhs. I simply do not care.