Add me to those who say travel agent.
First, travel agents can often find flights which would be difficult for non-professionals to find. If you have one flight or one easy connection, then this might not be a deciding factor, but for many of us, getting to where we need to be in Africa can involve multiple flights.
Second, a good travel agent can save you money. I have looked at prices for flights and for some reason, my travel agent can always find something cheaper if not both cheaper and better - and I usually travel business class. My travel agent will often come in a few thousand dollars below what I can put together. If you have access to something like SABRE, then have at it. For the rest of us, a travel agent is well worth it.
Third, and this is the reason which cinches it for me, if you have a problem while flying - flight cancels, you miss a connection, etc., there is a world of difference between trying to fix things yourself from the middle of nowhere and sitting back and waiting for the travel agent to email you a new itinerary. Like insurance. You might not need it, but when you do, you're glad you have it.
All of this depends on having a "good" travel agents. There are plenty out there who do the bare minimum and aren't really worth it (when you see how much they make . . . it's a wonder anyone does the job anymore). Word of mouth, experience, etc., are all good ways to find someone who's prepared to go the extra mile (no pun intended!) to get you where you need to be, when you need to be there, at the lowest possible cost. But in well over a dozen trips to various parts of Africa, I've never second guessed my decision to use a travel agent (and I make all of my own North American and European bookings, so it's not that I don't know how).