Copying a database to different servers

I have a frustrating task of trying to support a bunch of databases with one of my solutions.
There is a canned starting place in SQLite.
I’m looking for either code that can read a database and replicate it, or at least its schema in another OR a cheatsheet that shows field equivalents between the popular databases.

I know I can do it the hard way but I’m running into silly things like not being able to order by when using specific types of text fields in MS SQL etc. This is tedious!