my vote is to spend a year or two building an enourmous army up and then rolling through them in a final solution style attack. (by army I mean Infantry fighting vehicles artillery tanks and air defence I'm not sure we need a huge airforce as it's quite expensive)

While I am not in any advisory position, I'd suggest a compromise between the two.
Storm the west coast of Africa; regroup, resupply, stave off eventual retribution, then storm on again.

This would be easier on the army (aside from any freak reactions from other countries), leading to two or three relatively short campaigns over a very short one that could leave us potentially vulnerable or a very long, drawn-out campaign.

Let's tortoise this thing!

I suggest slowly. We don't want to end up pissing off the wrong person and end up having someone drop some nukes on us.

Get a medium sized African alliance to declare war on you, then take them out. After that, start consolidating before overextending.

I'm inclined to take the West Coast and maybe South Africa in one fell swoop, then regroup in South Africa. If, for some reason, our taking of the west coast didn't piss off everyone to the point of murdering us with spoons, we can take some of the more valuable central and East African Nations. But really, I think the entire value of Africa lies in it's western, resource-rich regions, and that's all we need. Taking anything apart from that isn't entirely necessary. So yeah. I say we go Blitzkrieg on their asses.

The African Invasion
 

May 4, 2035

At 0300 hours on a cold Christmas morning, 2033, I positioned our troops along Senegal's southern border, facing Sierra Leone, after recieving word that our mission was a go. We launched our invasion soon after and in two days we had control of the country. Their defenses were laughable.

http://img.photobucket.com/albums/v6...nary/sp200.jpg

I left our navy in fortify mode just offshore of our mainland, just in case things got hot.

http://img.photobucket.com/albums/v6...nary/sp201.jpg

After that area was settled, we continued south into Liberia, where we encountered our most intense resistance. Several other African nations joined in the fight against us, seeing the very real threat to their freedom approaching to the west.

http://img.photobucket.com/albums/v6...nary/sp203.jpg
http://img.photobucket.com/albums/v6...nary/sp204.jpg
http://img.photobucket.com/albums/v6...nary/sp202.jpg

Our losses were trivial, but the dead will be remembered. A couple fighter jets were shot down by Liberian rebels and a few dozen soldiers were slain, but it was worth it. Then Niger got involved.

http://img.photobucket.com/albums/v6...nary/sp208.jpg

I dispatched our northern divisions to deal with them, while the western divisions cleaned up the remaining regions of any countries that had dared declare war on us. The southern division was sent to the Central African Republic and the Congo, taking both without issue.

http://img.photobucket.com/albums/v6...nary/sp209.jpg

After that was all said and done, I checked the map to see who else was currently at war with us. Pakistan and Croatia were the only ones left. We invaded and took them with ease.

http://img.photobucket.com/albums/v6...nary/sp210.jpg

That's a look at our take. I am putting our troops on extended leave while our relations with the world heal. I hear west Africa is nice this time of year.

Surprisingly, Pakistan didn't nuke us and their only defense after fighting the U.S. for so many years was their air force. We also lost no treaties and our economy is on a steady increase. After a while we can continue this invasion, or consolidate and annex. The countries we took in the invasion are Guinea, Guinea-Bissau, Sierra Leone, Liberia, Cote d'Ivoire, Ghana, Togo, Gambia, Benin, Niger, Central African Republic, the Congo, Croatia, and Pakistan.

Niiiiice. Seems like the Blitzkrieg worked, ja?

I'm loving this. Particularly the taking of Pakistan and Croatia. One's gonna be an excellent staging area for our eventual Middle-East takeover and the other'll be real good for any conflict with the NATO.

What resources did we get access to as a result of our recent activity? I know that region is resource-rich, but I'm not sure who's got what... How's our budget been affected? Any sudden jumps in our surplus?

You said casualties were minimal, and that's good obviously... what mystifies me is that our international standing didn't seem to suffer too much. Is it just that people don't care about Africa, or did you do something covertly?

One thing I'm slightly annoyed at is that we didn't take Nigeria. That was sorta my primary goal in this campaign. Perhaps, once our relationships have improved we complete our conquest of the western coast, taking Nigeria, Mali, Cameroon, maybe Congo, and then perhaps just launching sporadic attacks against the other most resource-rich regions in central Africa and against the countries with the biggest military. That way we'll have the wealth of Africa on our side and won't need to worry too much about our new neighbors conquering it back...

Once we have a firm hold on Africa, I'd suggest we start amassing forces in Pakistan and prepare to sweep through the middle east.

Wait a minute, if we took Pakistan, does that mean we have their nukes?

I imagine Nigeria's the big boy in West Africa and could stalemate us into a prolonged war. Though Niger was initially my target because it has extensive uranium deposits, hopefully helping any nuclear program we've got going.

Surprisingly, nothing noticeable. Except our surplus has jumped by $5 billion, bringing us to $50 billion. We can easily afford a nuke program once things cool down.

I guess people just don't care. =/ I mean, most of Africa hates us, but the rest of the world let out a collective "meh." Though I'm sure that will change with a move on Morocco, Nigeria, or someone bigger like that. We should be cautious and swallow up the small ones first, then do some strikes on the big ones one at a time.

Unfortunately, no. But, like I said, we can research our own if you'd like.

[Edit] Also, the U.S. actually had troops standing by in case the war forced my back against the wall, which I thought was awesome. It shows they're at least serious about the alliance.