Except of websites with very small user base, the use of sqlite is not recommended as it doesn't provide concurrent writes. Mysql or postgresql is usually a good first choice, but web2py supports about 10 different DBs, so you can choose something else too.
The application code (including instant press) is using DAL, so it is not bounded to sqlite or any other any specific DB. It will work the same. By default it is sqlite and to switch to a different DB you need to modify the variable DB_CONNECT_URI at the top of the config file: http://code.google.com/p/instant-press/source/browse/models/_aconfig.py Read the book chapter on deployment: http://www.web2py.com/books/default/chapter/29/13 There are many options. It's hard to recommend one without knowing what your host constraints are.
