Do I have to use SQL Server?

Question

I am a long time programmer, but I am new to web site designing.  I want to create a web site that may have up to 5000 members.  I find ASP.net with sql server, makes creating a web site so easy.  However, Sql server express, I think only allows 2GB of storage space, and I will need more.  To get more I will have to upgrade SQL server at a cost I do not want to pay, until I know  my site will kick off.
In all my desktop applications that I have previously designed, I have always preferred to make my own databases. Prefferably storing the data as objects.  The databases I have designed were only for 1 user.

I was wondering if it is possible to make my own database system on a web host without going the route of Sql server?  I mean simply, not  programming a life-long project.
Also what major obstacles would be in my path if I did so? 
I am asking this now, so I do not get deeply involved in the project, only to find out it is out of my league.

Basically my site may have 5000 users.
Each user will have a profile.
Each user will add new information to the data base regularly.
The Data base will process and send back statistical information.

I appreciate any help,  thank you.