WaW: Sounds like you're already interested, so I won't say too much, other than I really enjoyed the campaign. Grenades are deadly in this game though.
MW3: If you've already played the previous two, it makes sense to finish the trilogy. MW3 is more of MW2, with all the Michael Bay-esque huge set-pieces and explosions. It's worth pointing out here that a lot of the criticism COD gets is unwarranted. People need to adjust their expectations. Some people have this idea that COD is supposed to be realistic or something and that's why it gets shit on on GAF (trust me, there are other flaws that could be focused on instead). Know what you're getting into. If you enjoyed MW & MW2, play MW3. If you didn't like the linearity then perhaps pass.
BO: THE NUMBERS MASON. Memorable campaign and a series favorite of many fans. Guns feel a bit plastic-y to me (see: Famas) but that's my only minor complaint.
BO2: Another sequel; decent campaign to begin with, but it ends very abruptly. You're better off just playing the first Black Ops.
BO3: Continuing the trend in BO2, this campaign is batshit insane. Difficult to follow. Skip.
AW: This really started to push the boost-jumping that has become a staple of COD in recent iterations for better or worse. While the multiplayer grew stale (fuck me for buying the season pass eh?), the campaign switched things up and remained engaging. Also, Kevin Spacey is one of the main characters.
Ghosts: Criminally overlooked. Another memorable campaign and goddamn does it deserve a sequel.
IW: I actually haven't finished the campaign yet, but the premise is good so far, and the set pieces are great (space, planets, etc). It's also the first COD to have optional side missions, if that's your thing. I've heard good things about the rest of the campaign.
I tried to keep my descriptions decently vague so as not to ruin or spoil anything.
But basically, you won't go wrong if you play the one you were leaning towards (World at War), and if you like closure and the classic formula, MW3 is solid.
If you haven't played it, Black Ops 1 is highly recommended, while its sequels get a pass from me.
Ghosts had lots of twists and turns that kept me engaged, and AW made me not hate boost-jumping (you will know quickly if that's your thing or not).
If you want multiplayer rundowns, I can give those too, but if you don't like linearization you may not enjoy them. CODs now strictly adhere to the "lanes" trend in shooters, whereby maps are really 3 lanes or funnel points where all the action happens. It may not be apparent at first, but it's one of those things that once you're aware of it, you notice it constantly. (that being said I do still enjoy COD multiplayer; the real problem nowadays is the monetization, but i'll leave that rant for another time)
From your poll though if you have Titanfall 2 you may want to stick to that for multiplayer (I haven't played it myself but I hear good things). Respawn Entertainment was of course spawned by former COD-gurus who headed Infinity Ward, who left after MW2.
Oh, and I don't play too much zombies but it's best played with friends, and it's a part of COD that gets better every year, to the point where the last few CODs have actual backstory to the zombie mode.
And yea "geo-mod engine" is a phrase I used to be enamored with growing up haha and while it impressed me then in a limited capacity, it probably isn't that stunning now.