Congratulations (I think?) on the new bike, and welcome to the forum. It looks like you have the right attitude regarding resurrecting your '87 TW. The good news is that TW parts are readily available and relatively inexpensive, the bad news is that the '87 is the first model year for TW's and the electrics are unique to just that one year.
Here is a good thread by GaryL that may be of some help to you:
Good luck and just reach out here if you get stuck or need some help.