I'm not sure if your bike has Keihin or Mukuni carbs. I am more familiar with the Keihins.
The carb bowl gaskets tend to leak with age. If the bike runs good that's all you need to worry about. If fuel is dripping out of the carb throats then you need to attend to the float valves. Piston diaphragms last a good long time.
Change the oil and filter. Be careful unscrewing the filter bolt. It's upside down and you wouldn't be the first to strip the threads trying to turn it the wrong way. If you get the filter from other than Triumph the large o-ring will be the wrong size. For your first time, get the OEM part. The large o-ring can then be reused several times.
You can order just the o-ring from Triumph, pn 3600025-T0301.
Check the valves and adjust as necessary.
The ignition coils are a common problem if you experience a cylinder dropping out. The crank position sensor (pickup coil) is a common cause of stalling when hot and restarting after time to cool.
Change the coolant. I like G-05 coolant. Tighten all the hose clamps. Make sure the fan comes on when it should. There is an over-temp light. You should never see it come on. Test it by grounding the wire on the temperature sender by the cylinder head coolant outlet pipe.
Flush the fluid in the front and rear brakes and the clutch. (There is no cable).
That's all I can think of at the moment... Should be enough to keep you busy for a while!
Oh! The carb bowl screws are JIS, not Phillips! DO NOT TRY TO REMOVE THEM WITH A PHILLIPS SCREWDRIVER!!!
https://www.amazon.com/Vessel-Megadora-900-Screwdriver-Original/dp/B000TG8OTY/?th=1