All skaters must wear some kind of gloves. These prevent abrasion from the ice and cuts from contact with blades. Knit winter gloves are fine for practices. For races in Canada, a non-knit glove is required for cut resistance. Baseball batters' gloves or all-leather work gloves are quite fashionable.
Sweatshirts are fine for practices.
For your first few sessions, you may use whatever you already have. But some people say you run the risk of snagging a toe pick when you lean over in a turn with figure skates. This might cause a nasty crash. Hockey skates don't suffer from this problem but the shape of the blade can promote poor technique. You can learn the basics of speed skating on either figure or hockey skates, but you'll soon find you want the glass-smooth ride of speed skates.