Good morning,
I have very little experience of SQLite so I am happy to be corrected, but my understanding of it is that it is a file access database library rather than a database server.
If you use a file access database library (which includes JET/ MS Access) and give it a simple query such as
SELECT col1 FROM table1 WHERE KeyValue = something
and then ask it to do the same thing again, it will reevaluate the whole query because the database library has no way of knowing that it has just done it. In practice and on small datasets you might see some performance improvements on the second and subsequent execution as the OS may have cached the areas of the disc that need to be read.
These sort of libraries can very quickly become disc bound, which is a problem for all hosts with servers and shared users, if you have your own server it's just your problem
A database server such as MySQL/SQL Server/PostgreSQL can be aware that this query has been run and return the result without executing the query all all, it can be aware of frequently use tables and indexes and choose to cache them in RAM and all sorts of other tricks to reduce disk access and processor load.
I have a VPS and I would hope that the hosting company is looking at accounts that have Access/SQLite type databases to make sure that they are not gobbling up too much disc access. As I understand it, the VPSs here don't get their own physical hard disc, so someone thrashing the disc using Access will affect the performance of my virtual disc.
I am curious why you want to use SQLite if MySQL or SQLServer is available? SQLite's strengths are it's free and it doesn't require configuring as a server process, neither of these seem to be relevant in this case.
My own personal view on choosing to host on Windows or Linux is in part based on the type of sites that are to be developed, I believe that Windows/ASP.Net/SQL Server is a faster development environment then Linux/PHP/MySQL/PostgreSQL but that ASP.Net sites require more resources. If you are confident in one of these two environment swapping to the other is no great hassle. Given that there are Express versions of Dev Studio and SQL Server I can't understand why you would develop on Linux and deploy on Windows though.
Bye
Ian