Will I be ok understanding the story if I jump straight to Witcher 3? I heard the game is incredible I just feel like the old ones will be a little too dated to really hook me.
Basically not needed at all. Keep in mind you'll be dropped in the middle of a fantasy setting, so there's a bunch of names you won't know, but the backstory isn't necessary at all to enjoy it.
Go for it, man. I never played the previous games, and while some characters you will know they have a more detailed backstory, they will give you the basics so you can get what are their relations.