Does Warhammer continue on from the first? ie. to enjoy the whole story do I need to play the first then second?
There's no storyline. In Warhammer 2 the Eye Of The Vortex Campaign is a narrative driven experience but it's still a sandbox and you don't have to play it. You can play Mortal Empires which is traditional total war sandbox.
Warhammer 3 has Realms of Chaos as a story driven campaign but it's meh. It's still a sandbox but at launch was very much riddled with issues. They've addressed some however it's only necessary to play to win as it gets you Be'Lakor as a playable Lord in Immortal Empires
Immortal Empires is again traditional total war and has an insane amount of content.
The only things that carry over between the 3 games are:
Blood Pack DLC, you buy it for game 1, you get it for game 2/3. If you got it for game 2 then 2/3
All DLC for games 1/2 carry over into game 3.
If you don't own certain or any DLC, in game 3 you may still interact and fight against them in the Immortal Empires campaign however you cannot play as them yourself, only AI, as well as not being able to recruit their units through the new outpost system if they become an ally in your campaign.
Hope this clears some stuff up. If you only want game 3 there's still a lot of content!