ASE is a bit outdated, but it'll get the job done. I'd not recommend it though; these days there are much better free programs around- GrafixGale being one of them. Make sure to check the "Great Big List of Paint Programs", you are bound to find something good in there.
From my experience every program that supports layers and has a good zoom and basic pen tools does the job, the rest is pretty much your own preferrence. Onion Skinning is nice to have (GrafixGale has it) since it makes animation a bit easier.