Wow, very well-thought out and passionate insights about the games. Thanks for your input, pulling the trigger on CC3!
gerwin79: Sounds like a good recommendation.
To really say which one, I should have tried them all, but I haven't... My answer is Close Combat III though.
Close combat 1 seemed really primitive, CC2 was a great achievement in game development, CC3 took it a little further and allowed for larger teams. Then after CC3 you might think things improve gradually with each release: CC4 and CC5 and the Matrix games rehashes: CC3-COI, CC4-WAR, CC5-TLD, CC(2)-LSA, CC-PitF, CC-GWtC. But note this; contrary to expectations things don't gradually improve. AFAIK There is no real change in the core game since CC3. Some things improve (especially things that do not involve the core game) , while some other small things get a bit worse (girly soldier behaviour in the matrix releases, where they forget the order you gave them + mistakes in the heightmaps thus lines of fire). Besides that it depends on what part of WW2 is featured in each game, but the games are moddable to such an extend that you can convert any of those games to another subject.

Hicks233: This is a pretty good summary. To add to that:
I've got reviews for CC3 and Gateway to Caen:
https://gamefaqs.gamespot.com/pc/96044-close-combat-iii-the-russian-front-pc/reviews/164016 https://gamefaqs.gamespot.com/pc/799671-close-combat-gateway-to-caen-pc/reviews/162050 CC2 had the most brutal infantry combat, lots of rushes and hand to hand combat. The structure of the campaign was interesting if a little confusing at times and having a range of forces to use was excellent. Has great explosions as well.
CC3 has the best sense of progression with your troops and a simple but effective campaign structure. The tank battles are excellent and the infantry are vicious. Weather conditions play a part in your strategy and it has a good selection of mods. The Eastern Front makes a welcome change also.
CC4 has lousy requisition options and the tank combat is pretty iffy. The shift to a winter setting is a nice continuance from CC3 and the snipers are excellent. Infantry have the same ferocity as in CC3. Strategic map is a bit iffy as well. Not a very good menu system either with a lack of information compared to CC3.
CC5 has the best I think range of mods. A simple and effective strategic map compared to CC4. Infantry are even more vicious, armoured combat is back to a good standard. It's on par with CC3 for me. Nicely sized maps, good range of environments and challenges make for an all round excellent entry in the series. The menu system is clear, effective and a welcome improvement on CC4.
Cross of Iron - avoid, you can get CC3 with Der Ost Front.
I keep on forgetting that I have Last Stand Arnhem. It's not a bad remake of CC2 but it's not quite as good as CC2 either. Map size and pacing can be a bit of a problem. Overall though it plays well enough and the night flares are a nice inclusion.
Gateway to Caen can be very good and very boring. The maps are even bigger causing pacing problems, the visuals are great. Infantry are better than they have been in previous remakes and aside from some questionable accuracy issues and tendency to throw tracks the armoured combat is better than previous remakes. There are some issues with vehicle pathfinding and their obsession with roads which have gotten more than a few vehicles blown up while playing for me. Still, overall it's not a bad entry in the series.