Nothing improves skating more than getting them sharpened if you haven't already.
Exactly, lowest entry fee is the best, if you find you're into for more than new years resolution month, spend a bit more and have a nice winter. I usually rent skates and have only not purchased some because my leg alignment is slightly too wonky to do it enough.
Same goes for snowboarding or anything that has rentals, let the discovery process happen in the least committal way possible.
I got a cheap pair of skates from goodwill, well on my way into week 2 now.
Once I know I got the chops down, I'm gonna go buy a nicer pair - but until then, can't beat a pair of $10 skates!