Do you still have the old software installer? If so, I'd install that on the new server first and migrate your database over. Most of the settings are stored in the database I think, so you should find most things migrate over in the database. The only file you may want to consider copying over is the web.config from the web root for SolarWinds. Once you've tested that, follow the upgrade path for your current version to the latest.
If you don't have the old installer but you do have active Maintenance I believe it is possible to download the older versions. I seem to recall there is a link under the green Download button for previous versions. Also bear in mind that, depending what your current version is, you may need to do intermediate upgrades first! See the readme files for more information.
I dont have the old installer, but I am assuming I can install the newer version(with all the liscencing) without any problems on the new server. My first step is to move the database over and then install NPM.
Correct me if I am wrong.
The danger you face is that updates can bring with them changes to the DB scema! This is especially true if you are on an older main version.
I would advise downloading the old version and installing first, then import your existing database adn give that a few days to test. Once you're happy everything has migrated OK, then you start to follow the upgrade path. This way you firstly ensure that the existing data and settings are OK, then you start to upgrade ensuring that your database gets the correct schema updates to ensure your database remains compatible with the latest version.
A lot comes down to what your old SolarWinds version is. If it isn't a 10 I really would advise starting at your old version. If you're on a version 10 you may get away without starting at your old version as i don't think the DB changes much within the minor version updates; but someone from SolarWinds is best place to confirm or correct that!