You need an interface to get analogue audio into your PC. You already have a soundcard, so yeh you could use a DI box, but that would be a bit crap.
A decent interface will be a lot cheaper and smaller than a big digital desk. You can normally get them with 2 mic pres built in, PCI or USB or firewire, and some extra analogue inputs etc.
If you want the physical feel of a mixer, get a controller. Behringer do a cheap one.
There's not much need for an actual mixer in studios these days (IMHO).
I think with the yamaha thing you would end up using it to record one track at a time (especially if you're tracking drums elsewhere), and then once it's in cubase you will use the mixer in there and basically waste the yamaha. It's more appropriate for live sound and recording at the same time IMHO.