I've made a couple of variable filters as tonecontrols in my basses, and for me frequencyvariation is the easy bit (even though it is a bit of a compromise), it's q variation which is tricky on anything but state-variable filters.
For a smooth frequency variation using a potmeter, you'll need a stereo reverse log potmeter, and those are somewhat hard to get. But ideally the two halves of the pot need to track wrt eachother well, and those potmeters are really rare/ expensive. With less well tracking pots the range will be less.
As for topologies, Sallen key is pretty easy to do, and you need only two opamp stages (one buffer). For an all out state-variable, you need four, but you get LP and HP and band-pass as a bonus, as well as independently variable Q. On musikding there's a small PCB layout with such a filter (although it's probably only wired for LP since that's what you need as tonecontrol on bass or guitar).
Currently, I'm looking at Fliege filters, easily variable Q with only two or three opamp stages, but the first try was a dud.
You can't easily switch between LP and HP on anything but state-variable filters.
Edit:
And I'm only talking about second order filters here, if you want to go steeper, you can put two in series, but frequency variation will be exponentially more difficult.
