Welcome! I probably don't have near the experience of many of the guys on these forums, but I have had the pleasure of keeping my TW going for about 10 years now.
If I were in your shoes, I would start with the unknowns before tearing anything apart:
- Do an oil change with filter as you don't really know what type or weight is in the bike.
- Get fresh fuel in it as you probably don't know how old the current fuel is.
I am assuming you don't really know what kind of maintenance was done by the prior owner or when. Check the forum here for some cautionary notes regarding the oil filter. Good Luck!