This is a survival website, and I figure overall strength is more useful for survival than is being great in one exercise. While 100 push-ups is a noble goal for motivating yourself, there are more productive ways to build strength. Being able to say you can do 100 push-ups is mostly for bragging rights. If you're like me, you care less about bragging rights, and more about overall strength.
Nowadays, for strength building, I mainly do Grease the Groove, instead of spending large blocks of time in the gym. Grease the Groove allows me to be more consistent. My main exercises are push-ups, pull-ups and dips. Once I reach a plateau, I inject a more difficult exercise variation. For example, search "push-up variation" on Youtube.
For overall strength, I think it's better to workout with many exercise variations. I have found this tends to make me pretty good in a lot of different exercises, and not exceptional in any one movement. My maximums are about 60 push-ups, 16 pull-ups, and 35 dips. I workout with different variations of these exercises. I think that's pretty good overall, but nothing for bragging if we're considering the exercises individually. By the way, I recommend Youtube for keeping yourself humble!
I feel like I'm building useful strength more efficiently by focusing on variety. I can also gauge my balance better. For example, I feel like my pushing strength is disproportionately stronger than my pulling strength. I'd like to increase my pull-ups to 20 reps max before I increase my pushing strength.