Having just done the first service on my Classic 350 at 307 miles I would say go for it and do the complete service including the tappets. Some tips from my experience.
Watch some of the YouTube videos on the subject. Not just one but several as each have their way of doing things.
Take your time, be methodical, the first time will take longer as you are learning as you go along.
Use genuine parts and keep receipts, document and take photos of your progress in case of need to claim under warranty at a later date.
Removing the tank connections is fiddly, the fuel line particularly needs fingers on both sides pressing the locking tabs hard in the confined space. The plug to fuel pump only has a tab on one side, remove wire from clip on fuel pump, remove protective cover from plug, press the tab with one finger and gently ease the plug out.
Move coil, loose plugs etc well clear and secure out of the way of the rocker cover. Ease the cover gasket out of the cover and leave on head, no need to disturb factory stuck part and with care can be replaced in cover after job is done
Remove spark plug, put bike in 4th gear, rotate rear wheel in normal direction of travel to set engine at TDC, no need to remove the crankshaft access cover on the crankcase cover. TDC is when arrow marked cam chainwheel is at top not the hole next to it as some video state. My tappets were really tight so its well worth doing.