Yep, that's exactly what I mean.
These headphones seem to be pretty well regarded as good for the price range for mixing as well. The plus side is you can use them for both tracking and mixing, though checking on your monitors is very important, of course. Primarily mixing and just checking on your headphones is probably going to be the better option, however. If you're going to be buying two sets, one for mixing and one for tracking, I'd probably suggest just pooling the money together and getting and one even better pair.
I can't comment accurately on open vs closed as I have no experience. I'll let others guide you there. I'm sure there could be some benefits to the open design, however.
Getting an average pair of open (assuming open are better) with an average pair of closed is probably not going to be as good as just getting one really good closed set which does the whole lot. If you're going to be doing lots of mixing on your headphones (usually due to noise restrictions) then you may want to just get the one really good pair.