Choosing a climbing route is one of the two biggest factors in your chance of successfully summiting Kili. (The other important factor is your choice of a tour operator). Kilimanjaro is not a technical climb, and the standard routes do not require any particular skill beyond walking. However, the challenge is in the very high altitude and its effects on the human body.
The atmospheric pressure at the top of Kili is about 0.5 atmospheres (or 50 kPa). This is only half the normal pressure at sea level, which means that for every breath you take, you only get half as much oxygen as you would at sea level. Your walking pace slows to a crawl, and every step is an effort. If you ascend too quickly to these altitudes, you will suffer the symptoms of altitude sickness, including headache, nausea, loss of apetite, and in extreme cases even death.
However, the human body is remarkably adaptable, and proper acclimatization will help you avoid altitude related problems. The key in acclimatizing is to ascend slowly, so that your body has time to make the physiological changes that will allow it to function properly at high altitudes.
Simply put, the longer your route, the more days you have to acclimatize, and the better your chances of reaching the summit. Some tour operators running treks on the longer routes (such as the Lemosho route) have nearly 100% summit success rate, while the average for all trekkers is probably less than 50%.
We highly recommend the Lemosho route, which is often done as a 9 day trek (7 days up, 2 days down). This route is scenic, relatively uncrowded, and long enough for acclimatization. Another good option is the Shira route, which joins with the Lemosho route on day 2 or 3.
The Machame route is probably the most popular climbing route on Kili these days. It is scenic, but doesn't allow quite as much acclimatization as the Lemosho route. The Machame, Lemosho, and Shira routes all share the final few days to the summit, as well as the descent down the Mweka route
For a less busy route, or one to do during the rainy season, you might want to look at the Rongai route.
The shortest and cheapest way up Kilimanjaro is usually the Marangu route. In our opinion, you should choose this one only if you're more concerned about time and money than having an enjoyable trek.