Do I need to play Starcraft 1 (?) to be able to function and get a good understanding of the game, I have looked into the game for a bit and It seems quite good, and I am thinking of getting it
Definitely not, first of all there are tons of former WC3 pros who never played BW at a high level and are now top SC2 pros - SaSe, Naniwa, basically all of the chinese players, NightEnD, etc. SeleCT didn't play either WC3 or SCBW. Some "lower-tier" NA pros like Minigun and Time have no previous RTS experience and are GM MMR equivalent. Personally I played SCBW very sporadically over the period of a few months over a year ago. Probably 30 games max and I was terrible, the bronze equivalent of SC2 (iCCup D-). Doing fine in SC2 since I'm supposedly in the top 2% of NA players after less than two months of playing.
Why: SCBW experience helps with your mechanics -- mouse accuracy, constantly making workers, hitting production cycles, not getting supply blocked, map awareness, etc. These are substantially easier in SC2 because of multiple building selection, unlimited control group sizes, automining, improved AI pathing, etc. if you played SCBW at a high level then you get a big head start, but since SC2 is much mechanically simpler, it's very easy to "catch up' in terms of mechanics - especially if you are just a casual player.
edit: Unit compositions are totally different, SC2 isn't just a prettier version of SCBW with a few extra units added. If that were the case, SCBW experience would probably help you understand SC2 a lot better... but instead SC2 players think of SCBW units for nostalgia reasons rather than to determine how to win in SC2.