The 8000m mountains are located in Nepal, Pakistan, and Tibet (China) with the heights ranging from Shishapangma at 8012m to Mt Everest at 8848m. There is a significant difference in climbing the lower 8000m mountains compared to the highest five – climbing with no supplemental oxygen feels exponentially harder for every step above 8000m!
Good objectives for the first expedition to an 8000m peak are Cho Oyu, Shishapangma, Broad Peak and Gasherbrum II. These four are at the lower end of the altitude range and their standard routes are less challenging than some of the others. But they should not be underestimated. For example, there is a low rate of success in climbing to the very top of Broad Peak as there is a long ridge above 8000m from the fore-summit to the true summit at 8047m; and on Shishapangma there is also a difficult climb from the Central summit to the Main summit.
Your choice of the suitable objective should take into account both your previous experience and the type of experience you are looking for. If your main objective is to submit an 8000m mountain then it might be better to go the standard route of one of the popular mountains in peak season (pre-monsoon in Nepal and the summer in the Karakoram). Your chances of getting to the top will be higher with several other expeditions out there at the same time; you can share the task of fixing the rope and you might team up with other climbers for a summit push.