Hello Westmann11,
welcome to SWAT forum and congratulations on finishing Crossfire Singleplayer!
For getting back home, you will need to take the following route: Banysia -> Belay -> Kinak -> Assris -> Sorror -> Trawtai -> Phanchdar -> Hyperspace.
In Hyperpace just dock back to the jumphole you came from, this will lead you to Menton system where you had been with Coalition guys earlier in the campaign, so you should know the rest of the way.
Prepare for making a looooong journey through Altair again - unfortunately it's the only way back.
- Wanderer -