If you haven't played Panzer General or Panzer Corps at all, I would recommend you to start with the basic game (Panzer Corps with the "vanilla campaign"). Don't worry about quality and length, it's plenty.
However, if you consider yourself an experienced wargamer, here's my input on your decision as well as my commentary on previous posts:
- The basic campaign does start earlier and ends later than Afrika Korps, that is true. And that does make for a slightly more interesting campaign start, since you get more crappy hardware to agonize over (and make interesting upgrade decisions over). But really it isn't such a big deal you might think - after all, PzIIIs are available already in 1939. The difference is mainly how your starting PzII in Afrika Corps is achingly obsolete already when you get it (as opposed to borderline useless but still not an immediate death trap as in Poland '39

) Do note that there is no Spanish Civil War start in Panzer Corps (unlike the old Panzer General, which was a nice touch).
- After playing Afrika Korps you will look at "regular" maps with disdain. Those grassy green hexes and their bountiful supply, pah!

(Desert hexes truly teach you to become a better commander; their reduced supply really does have an impact on the game) Desert terrain never becomes a chore, only a challenge.
- Like said above, the core game engine is the same for both PC and AK, including the AI. The reason you might perceive the Afrika AI as better is because the campaign was developed later, and it does take advantage of the massive scripting improvements of the scenario editor (introduced in patch 1.10 I believe). So while the AI isn't actually better, the scenario design sure is. (Again, this should only factor into your decision if you have prior experience with this sort of game).
- Multiplayer wise I think it is a wash in terms of number of scenarios.
- Do note that you cannot play AK scenarios using PC, and you cannot play PC scenarios using AK. All scenarios are delivered in both games and can be examined in the scenario editor, but each scenario is hardcoded to a particular game and cannot be played with the other: you get a "Cannot start game because content package missing" error message. (Meaning, for instance, that the Crusader scenario is only for Allied Corps even though it features pretty much the same desert terrain as Dash to the Wire, the corresponding Afrika Korps scenario).
- For multiplayer I believe most if not all popular maps are duplicated in AK. Meaning that the Hylan Valley scenario is accompanied by a Hylan Oasis scenario. AK won't load the first one, but it will load the second. I don't know if you can play Hylan Valley against a MP opponent if he or she has PC and you AK.
- Obviously more people have Panzer Corps, so if MP is a major concern, that game is definitely the one to get unless Single Player restrictions (including hot seat) are not present in MP...
- For some people, getting to face the Soviet one day and the US the next is a plus. For others, it's a jarring experience. Depending on your views, facing mostly the British in Afrika Corps is then either a positive or a negative. (Obviously, the Grand Campaign DLCs solve this for the vanilla campaign, but still)
- For some people, being handed Italian units is a major irritant. For others, it is an interesting challenge! Let me just say that you don't have to use Italians any more than you want to - this fact alone should not deter you from choosing Afrika Korps.
Hope that helps...