Which destiny game to buy?
There is only one Destiny "game" at the moment.
The difference is that you can either buy just the base game, or you can buy the legendary edition/Taken King edition, which also includes all 3 DLCs.
Buying the base game would be cheaper on it's own, but you will have to pay even more to get all the DLCs (you need both year 1 DLCs to buy The Taken King). This would be more expensive than just buying the Legendary edition in the first place You are also limited to select activities which excludes most current "end-game" features. Without The Taken King you will only be able to level to 34, while the current max is 40.
Buying the Taken King edition gets you all the DLC for a bundle price, and is the cheapest way to go if you want everything Destiny has to offer. If you have friends that play Destiny, or have tried playing before and really enjoyed it this would be the best option.