DS2 can give you a bit of insight on some of the characters in DS3 and how you wound up where DS3 takes place, but be warned, you may just feel less impressed with DS3 if you play DS2 first. It's not at all as much of a generic shooter as DS3 as implied.
DS2 has detailed vs universal ammo, and there's less of it to find, so it helps to grab things and throw them when you can. It also has WAY better map variety and better mood and atmosphere.
DS3 by comparison is long and boring.