Here's a link to what I did to get a dedicated server setup using TADST. I have a post there with some steps for you to take and videos for you to watch. My handle there is the same as here: https://forums.bistudio.com/topic/159708-alive-advanced-light-infantry-virtual-environment/page-342
For the most part, persistence works really well! In the ALiVE Player Options module (pretty sure that's the one, not near my PC), you'll want to be sure everything is set to "yes" for persistence. Just make sure once you're done playing the mission for the night, you login as Admin by typing "\#login yourpassword"...without quotes, and then select "Admin Server Save and Exit."
Not everything a SP vanilla save and load will be there when you restart the server (you'll have to ask a dev to clarify what exactly persists and what doesn't), but everything you'd need to feel like you were actually continuing a mission works wonderfully with War Room (things like time of day, player position, ammo count, cleared bases, ALiVE markers, etc. Though note I prefer to spawn back at base upon reload because at the moment, AI teammates' position don't persist. So I like to spawn with them back at base).
I haven't had a more rewarding SP experience with ARMA than I have had with ALiVE. I really don't touch other game modes anymore. Well worth the setup.