Also, to Drummerboy, you'll get lots of advice about what bikes and gear work best, and it's all good. But everyone's commute is different, and everyone's personal subjective preferences are different. I like high drop bars, someone else likes low flat bars--telling you that won't give you the answer to what will work for you.

Here's my advice--ride your Fuji as is and then decide what you need to add or change before you spend the time and money to make major modifications. Vintage lightweights make good commuters, IMO. Things I like for a commuter are the ability to add fenders, wider than 23mm tires (I like 700 x 28--35, depending), and the ability to carry a modest load. Lots of different bikes can do that, including, probably, your Fuji. And some get along fine without any of those things.

If I could even remember all the bikes I've used for my 13.5 mile commute in the past 15 years, it's a long list--Raleigh DL-1 Roadster 3-speed, Raleigh Sports 3-speed, vintage Dawes fixed gear, Schwinn Collegiate, Schwinn Heavy Duty (coaster brake middleweight made for use in factories), vintage Raleigh Super Course, early 70s Bottechia Professional, Trek 400T, 2 different Trek 520s, Airborne Carpe Diem (CX), Mercian Pro, Bob Jackson Special Tourist, Lotus Eclair, Bridgestone RB-2, custom mountain bike, cheap hybrid, etc.--and I've left some other vintage lightweights out. I liked some better than others, but all of them worked.