I'd say to watch your tension....it's soul destroying to have to pick and stretch each stitch to winkle the hook through
...i'd also recommend a smaller hook, it makes a chunkier (but less tight) stitch with a fatter yarn and is easier to get into the rhythm of wrapping and the in and out motion.
style craft/woolcraft dk is fine and I'd also not bother with learning the foundation double crochet...I've managed all these years without it!
UK and US stitches are the same, it's not a different technique, they are just called different things.
UK have slipstitch, chain, double crochet, half treble, treble, double treble
US have slipstitch, chain, single crochet, half double crochet, doublecrochet, treble (= to our double treble)
Also, really look at the stitches, they are similar to knitting, in that you have that little v shape, but in knitting it is two strands, and stacked vertically and in crochet there's three strands, and you sort of ignore one, and they are horizontal.