IF anything buy them a PS3 a PS4 would be pretty much be a waste of money. its cheaper it does NOT need you to pay a monthly fee to play online and more of your kids friends already have that console.  (btw I do own both a PS3 and a Ps4 but just because it was 265€ and since then it is a paperweight and is waiting for jrpgs or good exclusives)

Also there is 1000 good games compared to the 2 or so on PS4. And if they mainly want Minecraft and Fifa then why buy a console thats 2.5 times more expensive? (Btw minecraft on console is really crappy compared to PC so just buy Fifa for PS3 and keep playing minecraft on PC  you can do 1billion times more things with the PC version compared to the limited PS3 version. (I own both versions. Why do I own the pS3 version when it is crap? Because it was free last week)

By the time your kids will have lost interest in the PS3 the PS4 will be 200 bucks and will also probably have 100 good games. (and I would wait for a slim PS4 anyway. New hardware always is untested and has more problems)

You should consider this.

The future is on PS4 and it's slowly getting more and more family games both indie games and first party games like Hohokum, LittleBigPlanet 3, Tearaway Unfolded and Ratchet & Clank. While PS3 has a HUGE libary of games.

This is going to be a difficult decision, I can see. And it looks like we're going to have to choose between which group of friends they will be able to play with online. Thanks for the input so far, and for any more that follows. It has given me plenty to think about.

False, please don't spread false information.

EDIT: Thought you said can instead of can't. My mistake, sorry.

PS Vita

*quickly runs away*

I say go for the PS3 because it's more affordable, has free online, and has a much bigger library. PS4 still needs some time to establish its library.

Ignore everyone telling you to get a PS3.  The two games you listed have much better support on PS4.  If they want to play with their friends they need to get the same system. PS3 and PS4 do not have cross play support for almost every game. 

Go for a PS3 for now. Game library is huge and you'll get a LOT of game for a very cheap price.

All i read was "friends" "friends" friends" "friends".

If that is the case then you should get them a PS4. Some of there friends may already have it or most of them will be getting it for xmas as you pointed out. N point buying a PS3 for them now unless you plan on buying them yet another console in a year or so from now. Just go with the PS4. By this time next year no one will be talking about a PS3. And if I know kids at all... having a PS4 will give them a lot of "cool points" in school. It sounds silly I know, but those things are important to kids lol.

As for what games they would play on the PS4 besides Fifa and minecraft, well it would be either Little big planet or racing games. There are a couple of other games (indie/retail) with comic violence or none at all like Journey, flower, The witness, Rime...etc that they maybe able to get into. As it stands I have your kids pegged at 7-10yrs old. They will grow with the console.

Get them the PS4. You may even enjoy it yourself :)

edit:
and pleae, ignore everyone telling you to get a PS3 cause its cheaper and has a bigger library. That kinda logic sounds more like being penny wise pound foolish to me. If you want cheap for the PS4 then wait and buy games used. But for the reasons you mention and for the games they seem to be into then buying the PS4 would be your best bet. So you get a PS3 and they play Fifa witheir friends this year. what happens come january when most of those friends have got a PS4 for xmas. And the rest of them are following suit through next year. Do you want your kids to be those guys that just picked up a PS3? Would you be willing to then spend money (again) to buy them the PS4? The advice most of those users are giving you, are things even they wouldn't do if they were in your shoes.

Hmmmm.... Hedra42, I think you should put up a poll so you can get a good general idea of how many people suggest PS3 vs. PS4.