For those who actually run stuff like this, this question is very naive. We could flippantly say, "A bajillion dollars," but that's not going to help you.
You need to answer the following questions and once you have those answers, finding the answer to this question is easy enough:
How large a database? Petabytes? How much data are you storing daily? How do you want to store that? Postgres db? Hadoop? NoSQL flavor? And that's a factor of the app you are creating. Django? Javascript? Ruby? Scala?
Do you have a mock up of the app? Or at least a clear idea of what kind of data you want to capture and feed into those ginormous data stores? That's going to tell you how long it's going to take to code it. Hope you have friends that work for free to help.
You can find service providers to do anything for the right amount of money. You need to ask yourself, is the data served going to be available 24/7 or just certain hours of the day? Do you need the compute power to be heavier certain parts of the day? For lots of data (petabytes) it's likely more cost effective to have a pair of data centers that are storing that data. You likely don't need to have every bit spinning on the quick online access.
Know your app and what it is going to store. Calculate the 100,000 users per day times what the app uses for data.
We can't give you cost estimates because you essentially asked something without any data in it to judge it by. I'd suggest getting an AWS or other cloud account and trying to build the mock up of the app on a small scale. That's going to be an excellent learning experience.