New bike/fazer owner, proper way to go about the initial service?

[kgjersda]

Pump up the tyres and check the bulbs?

All new tires on it, but I will be sure to check the pressure. Bulbs are working

Check/adjust the TPS along with the carb balance to get rid of the rough idle.

Will do.

Unless the coolant is discoloured, I would be tempted to not change it.

Service manual states that it should be changed every 2 years? I cannot be sure it has been changed in the last 6.

I would recommend, whenever you need to, to upgrade the fork oil to 15w oil instead of the suggested 10w, which will noticeably improve the handling.

Noted.