Grease the skid, and look for abnormal wear and binding. The skids will wear prematurely if they are not maintained. They like lube.
Ski rubbers.
Oiler setting. If you have a shop manual, you'll know how to give it a look. Turning it up, if it isn't, is up to you. But find out what it's set at now.
I would crack apart the secondary and check bushing, rollers, helix, spring, looking for abnormal wear, galling, spring binding. Cheap insurance.
If the belt is old, and most used sleds do not come with new belts, I would drop a new one on it and set deflection.
If you don't know the fuel filter condition, put a new one on. I do spend other people's money well, but you asked.
Check throttle free play. It's adjusted up top, above the hood. Simple barrel adjuster. It's in your shop manual.
You know about the VES, primary, and chaincase. Good luck, enjoy.