I don't know a lot about Klaassen, but I've always had him pegged as being fairly similar to Davies.Davies Gana Rooney
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From the little I've seen of Klaassen, they're both players who don't touch the ball an awful lot for midfielders, but have decent movement, support attacks and try to help out defensively.
I'd love to see what he was like in our most recent midfield 3 next to Gueye and Rooney at some point.
Otherwise, I think you've got the priorities spot on. Though I'd be buying a replacement for Rooney, rather than a back up.