Database Development

You did not mention what DB product you want to use, so I will assume MS SQL Server.

 

You can host it on MS Azure quick and easy. Many other cloud services provider like AWS also offer it.

 

for estimation, there is no particular tool

 

you have to design by per table basis, then you can derive size per row per table, and estimate no. of possible rows, then sum all tables

 

but its hard to exactly derive your DB size until your application is in actual use