No, the DLC is not necessary to play! We have designed the DLC especially to just be a fun variant rather than a necessity. It is definitely not pay to win and we would never want to split the community like that.
However, most players do find it fun to have a wide variety of cosmetic options - the beauty of Helldivers is that you can mix and match many different loadouts. If you do want to purchase DLC, the Mega Bundle comes highly recommended by the community.
If you need help deciding or want to read up about the DLC, you can always visit the forums or look at some of the play guides :)