I've been considering purchasing the basegame of Tannhäuser, but is it recommended to get the Revised Edition rulebook right away as well?

Yes, it is recommended - but you could also look for the basegame of Tannhäuser with the revised rules included (a red sticker shows this, I think)

Azanael said:

Ah I see, so those boxes come with said rulebook already included, or is it just a slim version of it?

Yes, if the box has a red sticker "revised Rules included" or something like that on it, the Revised Rules should be included.