Regarding campaign play Sgt Jasper and KAreil are correct that the operational series(ModernCampaigns, FirstWorldWarCampaigns and PanzerCampaigns) have scenarios that are depicting a whole or a part of on operational campaign, I can add to this that in France '14 there is an attempt to make a "Grand Campaign" by modifying the operational campaign scenarios and that not only within France '14 but also in East Prussia '14.
Take a look at
http://www.hist-sdc.com/spotlights/fwwc_f14.php and check out the Designer's Notes under Game Documents, that should give you the details.
The tactical series(Napoleonic, Civil War, Early American Wars and Musket and Pike) has a campaign engine that links some scenarios together, usually depending on the campaign there are many or few choices to make and for each choice there is a corresponding scenario, the result of this will have an impact on the next scenario played within that campaign.
Usually you can expect that the scenarios, no matter if it's a game from the tactical or operational series, are made for H2H play mainly unless noted otherweise, some titles have special variants of the stock scenarios that are adjusted to play against the AI, this is more often the case on the tactical series(Napoleon, Civil War, Early American, etc.) than on the operational.
Anyhow just go for a title/series you find most interesting, no point in toying around with anything else as it simply won't bring you through the learning part of these games.
You should also look through this webpage, it has a bit more to provide on most titles than the John Tiller Software webpage.