One thing about the glory of knitting… if you’ve been told to knit more tightly, and that just isn’t your style, try smaller needles than you would otherwise use, by at least a size or two. This will tighten up your fabric, but still allow you to knit with a more or less regular tension.
Case in point: I tend to knit my socks with one type of yarn, because I love it; Lyon Brand Fishermans Wool. The reccomended needle size is 9. I knit on size 3 needles. This gives me a much denser stitch, better for soxes. The stitches do naturally want to be tighter than I normally knit, but without my changing my knitting style. It happens all on it’s own.
So, if you find that tighter/denser is better, try smaller needles instead of tighter sitches.
Oh, and I’ve used cotton for kitchen things and LOVE IT. I had a pot-holder-less house hold (say that ten times fast…) for the longest time until I was in a grump and cranked out some pot-holdery goodness because I was temporarily fed up with all my projects. Took a second to get used to then BLAMMO! beautiful yellow cotton pot holders.
Couldn’t have done it without cotton!