Hilda said:
pick the one that's got your favourite colour on the cover.
seriously that's all it takes
but imho you can't go wrong with getting the latest non-remake pokemon game, so start with X or Y.
aside from the plot, its a solid iteration that has heaps of pokemon to catch and places to explore until post-game. X and Y also introduced a bunch of things that made the game much more friendly to newcomers, so it really is the best starting point for now.
after that, try playing one of the Gen IV games for DS, preferably Platinum. It has less Pokemon than the new games and sprite graphics, but you'll likely appreciate the story and content
so much more because its handled really well.
HeartGold/Soulsilver are a good follow-up to that because they're the best remakes GF has made, period.
All of the Gen V games are great but they should really be experienced after Gen IV. They would be Black/White, Black2/White2.
and from there just play whatever. i'd recommend Emerald somewhere down the track unless you'd rather go for the Gen III remakes.
tl;dr:
X or Y
then Platinum
then HeartGold or SoulSilver
then Black, White, Black 2, or White 2
then whatever
again choosing which version you want solely depends on whether you want to catch the thing on the box or not
either that,
or you just wait until Sun/Moon come out and jump in then because those are gearing up to be some really good games that will blow X/Y out of the water