@robine_k, doing this retroactively is a bit difficult as you describe, but you have the general idea. You will need to page through statuses/user_timeline for each user until you have the Tweets you require. To work within rate limits, I usually do some calculations up front and insert sleeps in my loops and just let it run as I go about my day.
The best way to do this and what we usually suggest is not doing this retroactively, but in real-time. Use the statuses/filter API to pull in Tweets in realtime and save the relevant data to a database. You won’t have a large data set right away, but you will eventually. This removes any concern over rate-limits. I’m not absolutely sure if it will support 100 users, but I just asked someone on my team and will find out.
If you are building a product or a business around this, just make sure you have reviewed the developer terms of use carefully. If you absolutely need all inclusive historical search and you have a healthy budget, check out Gnip for enterprise grade Twitter APIs.