The 100-pushups program is great, it'll tell you exactly how to start off based on how many you can currently do, and it'll give you exact set/rep plans for each day.
The grease and groove thing is great, just be sure you aren't ever going to fatigue. If you don't want to do it every hour, a good thing to do is every day do a full set up to around 80%-ish of your max reps. If you max out every day you'll overwork the muscles, but if you do a pretty good amount without hitting your max, you'll teach your nervous system how to increase it's work output, and increase muscle endurance.
Since you're going for 90 in two minutes, you aren't doing any weighted pushups or trying increase muscle strength, you're just trying to increase your muscular endurance. Pushing them to 80-90% tops is a great way to do this, I would at least one day a week though. It's okay to test your max number or go for as many as you can do in two minutes once a week or every other week, but doing it too often puts too much stress on your nervous system and you won't recover adequately.