Modern components will fit just fine, because the bike already has them. The bike probably came with Shimano 105 or Ultegra (600) components. It will have the same hub spacing (130mm rear, 100mm front) as current road stuff. Probably already has STI shifters, though possibly down-tube or bar-end shifters. Very likely the components are 8-speed. Wheels are definitely 700c.

Only substantive difference compared to current road-bike stuff is that this 1500 will have a threaded headset and quill stem instead of a threadless headset system. Threadless can be slightly lighter and moderately stiffer and is more difficult to adjust the height, definitely not worth changing out unless you need a new fork anyway. In that case, 1" threadless headsets and stems are still available.

I would say, though, that unless parts are worn out there's no need to replace anything, unless you really have a hankering to get 9- or 10-speed drivetrain. But since you're just getting into road biking, I'd say that if the components work well (or will work well with a tune-up) then just use the bike as-is. The difference in function is minimal aside from having slightly wider range (or more closely-spaced) gearing.