New players may wish to play through the previous entries in the Total War: Warhammer series first to experience what they have to offer (as the games are certainly still worth playing), but it's ultimately not necessary - and in some cases could even be detrimental.

Do I need Warhammer 1 and 2 for 3?

Do I need to install all three games to play? No; as long as the other games are in your library, you only need to have Total War: WARHAMMER III installed to access Immortal Empires.

Will Warhammer 3 require Warhammer 2?

You do not need to own Warhammer 2 in order to play Warhammer 3's main campaign. However, you will not get access to all of the features, because the main campaign, and Warhammer 3's downloadable content (DLC) are completely separate. This means that you can enjoy Warhammer 3 without purchasing or playing Warhammer 3.