I'm switching sever hosts in minecraft but dont want to lose the progress from my current server, is it possible to move my world?

Yes you can, most server hosts should allow you to access your server files, from there just copy all the important files like permissions, the world file, the data file, etc, and move it to your new server, but if you are going to be using mods you might just want to restart as most mods use world gen, so I think if your going to use mods, just restart, or only keep the player data file, which should save all of the items you have in your inventory.