what do I need to look for when buying running and pull up gloves?

a same pair for running, yoga, pilates and pull ups and other core exercises in winter.

what I use now are regular leather gloves. While thin for leather, they're a bit stiff sometimes. I was wondering if there's something out there that might be better.

When it's temperate I don't use gloves, function is mostly to keep me warm while I train.