For that kinda age, clean the carb, drain the tank and install an inline fuel filter. Carb work is always hit or miss on bikes, but there are plenty of resources to help you avoid missing. It's almost always a lack of diligent work that leaves somebody scratching their head with a carb.
After 10 years, the tires are gonna have to go, no questions asked. Don't expect a safe ride on the road with them.
As well, before you even put the bike in gear or try to start it, give it a day with some oil in the cylinder and then slowly roll it back and forth in 5th gear.
You'll probably need a chain and you should adjust your valves and cam chain.
It's also gonna need a battery.
Do that stuff and you'll be on your way. Just read up on the issues of owning an '87 on here. It's a special needs year, but just as fun as the rest.