Which gaming account should I get/setup for my teen daughter?

Here's the background...
So, I tend not to play video games at all any more (not for at least 15 or 20 years). My teen daughter wants to get a Playstation gaming console...but it seems less about playing and more about socializing with her friends. Her friends - while i promised my partner not to call them 'idiots' - are not really the best decision-makers and they're quite affluent (and we definitely are not affluent), so their poor choices usually never impact them. (I think it is less about being teens, and more about them being rich, entitled poor decision makers, because my daughter and a few other poorer friends are actually good kids who know that we can not get all the things.) Here's an example: all of my daughter's rich friends will ask their parents to buy them widget X, and so of course my daughter wants one so she can connect with these rich teens. For these rich kids, after they inevitably abandon widget X, there is no issue; they merely drop them off in one of the rooms in their mini-mansions. But for me, i can not always afford to buy widget X and then have my daughter abandon stuff in our little, meager but love-filled house. (Please if possible let's avoid the topic of how I'm raising my daughter, because all of the parents of us poorer kids in town have the exact same issues with our kids.) Now, we come to the part about my daughter wanting a playstation...I don't mind saving up for a PlayStation - especially if she'll use it...However, since she really only wants it to socialize with her rich friends via a couple of games, i was thinking on getting a PC/gaming rig (not as expensive as PS or some sort of AlienWare) instead of the dedicated gaming console, but still plenty usable for some games...So that, after some time if she abandons it (because for example her friends have migrated to other avenues of socializing), i can always re-purpose the machine. In my mind it seems a more worthwhile investment. (I'm a software guy mostly, but over the decades, almost every machine i have/own has been franken-built by me...so i know just enough hardware.) Now, if I go the route of a PC/gaming rig, can i just sign her up for online gaming accounts like PlayStation Network, and that will suffice for her to use her PC but still connect, say via PSNetwork, with her friends playing PS games?? (To help, i should clarify the games these teens play are fortnight, minecraft, and grand theft auto...I think GTA does not support in game chat/comms with friends, though i could be wrong.)

So, is it possible for me to sign up my daughter on an online gaming account - like PS Network - that would allow her to communicate with hr friends? And, if so, which gaming network should I set up an account, PS Network, Steam, etc.??? Thanks in advance for any suggestions!!!