I'm not familiar with the '87 Trek Elance but if it's comfortable for you to ride long distances, then it should work fine.

As someone suggested, you'll need to get a spare tube or two to carry with you, maybe a patch kit, tire levers, a multi-tool is good to have, and some way to air up your tires. I carry a C02 inflater because it's cheap and small.

Lights and fenders are a good choice for a commuter.

Also, you'll need some way to carry your stuff. You can read a million discussions/arguments over which is better. A lot of people like racks and panniers. Others like backpacks and then others go for messenger bags. Personally, I carry a Chrome Metropolis (messenger bag) and love it but you may not. Whatever you carry, make sure you're comfortable with it and that it'll keep your stuff dry in case of a surprise storm.

A good lock setup (U lock and cable lock used together) is good to have if you plan to leave your bike anywhere unattended that's not secure.

And bring plenty of water and snacks in case you need them.