I would very much like to play this one. Should I bother playing the ones that came before X and Y and after Yellow? Would I be missing much?
There's a fair amount of new mechanics and stuff, but the overall system hasn't changed. You did miss some stuff, but it shouldn't be that hard for you to get used to certain things. Here's some of the more major points;
1: Moves used to be designated as physical or special depending on their type. Now it's determined for each individual move. For instance, Sludge is now a special attack, but Poison Sting remains a physical move. Likewise, Thunder Shock is still a special attack, but ThunderPunch is now physical.
2: Each Pokémon now has an Ability that can affect battles. For instance, Weezing has the Levitate Ability, which gives it an immunity to Ground moves. Arbok can have either Intimidate or Shed Skin- Intimidate lowers the foe's Attack when the Pokémon enters the battle, and Shed Skin gives Arbok a 1-in-3 chance of healing off any status conditions between turns.
3: Pokémon can now hold items which can influence the battle. For instance, if a Pokémon holds Black Sludge, it takes a little bit of damage each turn, unless it's a Poison-type holding it, in which case it restores HP instead.
4: There have been three new types introduced since you last played- Steel, Dark, and Fairy. Magnemite and Magneton are now Electric/Steel. Jigglypuff and Wigglytuff are now Normal/Fairy. Mr. Mime is now Psychic/Fairy. There are more that are now Fairy-types, those are just off the top of my head.