Mont-Blanc range can keep a climber busy for its whole life, I guess. You will have to cope with the conditions, however, and it is not easy to make plans in advance.
Weather is quite unpredictable.
Here I list what I consider to be the very best climbs of the range. Some of them are very demanding. If possible, you should try to do one route on Mont-Blanc. I have always liked them a lot and find they have something special, because of the high altitude, length, and very glaciated conditions. At 4807m Mont-Blanc is significantly higher than the other peaks in the range, and the Italian side is very steep, complex, and quite uncrowded, since it is freqented only by experienced alpinists.