You can have fun with the base game by itself...You might want some of the DLC characters though. The Mechromancer can be kinda fun. I would say hang on and see if the game gets a flash sale and get the full thing if possible though... --- http://raptr.com/badge/arleas/uc.png http://www.speedtest.net/result/2868545294.png
grab the goty edition in a sale. The story dlc for tiny tina and the one with torgue are great and the extra characters are really good as well (I even prefer krieg over the base game characters).
The head hunter dlc's are good for the price (not included in goty) they are quite small maybe an hour or two of quests plus a repeatable raid boss; so if you enjoy the game it is fun getting these little extras if you play through the campaign and the story dlc and find you want more new quests.
Also not to discourage you from buying another copy of this great game but I am pretty sure there is a way to get split-screen to work on the pc version. --- Xbox GT: Zarosian 3DS ID: 1848-2118-1570 Origin and SteamID: Zarosio