I am still in the process of really discovering CoH, but these boards tend to be very quiet, so ill give you my thoughts.
COH is an excellent turn based tactical game. There are plenty of reviews so I won't bore you. Solitaire is ok but the AI is pretty poor. So far I have won every time by miles. There is a a multiplayer on line option but the online forums and boards are usually completely empty, so you will need to link up to get a match via this forum or BGG. I had a GREAT experience on line with a very good chap.
It is pretty much all scenario based with a very limited random option, though you can design your own stuff.
Bottom line... This is a great game but won't meet your noted criteria.
If there is a demo, try it.
A recommendation that meets your needs exactly, but is not WW2 would be Battle for Wesnoth. It is turn based tactical war with linked campaigns, troop selection and development, random maps, AI, multiplayer. It is fantasy medieval but plays like Panzer Corps in a strange way. Don't let the skin put you off a great game. AND IT IS FREE FOR PC AND IOS.
< Message edited by fentum -- 1/20/2013 3:30:57 PM >