The only similarity it shares with Pokemon is the collecting aspect. The gameplay is very different, but I would bet they'd still like it.
Older figures are always compatible with newer sets, but not vice versa. So a figure from Skylanders: Spyro's Adventure would work with Giants and Swap Force, and a figure from Giants will work with Swap Force, but characters new to Swap Force will only work with Swap Force. The only "sort-of" exception to this is that some characters in Giants/Swap Force packaging will work with the older games if that character already existed in that game, and the Giants/Swap Force packaging is just a reissue.
If in doubt, make sure to check the packaging, as that will let you know which ones work in the older games. As an example, a character introduced in Giants that was reissued for Swap Force would have a green compatibility check for Giants and Swap Force, and a red x for Spyro's Adventure.
The other thing to look at is the element the character represents. Certain gates in the game can only be unlocked by a certain element. If you're not looking to spend too much money, look for the elements on the package to avoid buying characters they won't necessarily need. There's eight elements total, and each starter set has three characters each of a different element, so the minimum of extra characters to buy to unlock every gate would be five. That's the basics of it without going into too much detail which might be confusing. It's important to note though, the entire main game story is able to be beaten with just the starter figures. You'll just miss some side stuff is all.
My personal recommendation would be to just pick up the newest game, Swap Force, since there really isn't much story continuation between them (I think), and that way you ensure that whatever character that gets bought will work with the game. Check Walmart for Swap Force. I picked it up on sale earlier this week for $37 as part of their pre-Black Friday sale. Had to price match at Target though, since Walmart was out of Xbox One copies. There's also going to be some figure sales this Friday. Toys R Us has a buy one, get one 70% off deal, and Amazon has B2G1 free.
Edit: Correction on the Amazon deal. It's Thursday, and starts at 3:10 PM PT, and is just for Swap Force figures.