I learned my lesson with Counterstrike online on the PC; little buggers were just too much, they played all damn day and you could tell. Frustrating. You want to beat them? Get one of your sons on it- its the twitchy reflexes that you need that we no longer have at our age.
If you want a good shooter with offline aspects, a good storyline and relatively short campaign, any of the Call of Duty titles will do the trick. Ghosts was ok, Advanced Warfare had a more engaging story (might be because Kevin Spacey figured heavily in it) and Black Ops 3 had a good twist to it. Plus, you play as a rocked up soldier/specialist and unlike previous titles, you get to stick with your protagonist as opposed to switching bodies/teams (previous titles had you serving with different agencies as different soldiers, was a bit disjointed imo). Want something with a little more depth and drama, I'd go with Battlefield: Hardline. The Battlefield series on the whole was initially developed as competition with CoD and Medal of Honor; with Hardline they went a slightly different route and made it into a police crime drama. For my part, it made it much more interesting to play as there's more of a story and the voice acting is excellent. Prior to this entry, the Battlefield series was about being explosive, with set-piece action elements and gorgeous visuals. Battlefield 4 is the culmination of that mindset- its a beautiful game, like playing through an installment of the Expendables movie series, heavy on action and light (in this case ultra light) on story. In fact, I couldn't remember why I was even doing what I was doing but hey, blow up bad guys with awesome weapons and vehicles. Of them all, Call of Duty does that the best but its always worthwhile to have a go at the other ones too.
Congrats on the new PS4...I'm still debating on whether or not to upgrade my PS3 but I only use it for PS exclusives that I like (Gran Turismo mostly) and as a blu-ray player. I have the XB1 and love it.