First, welcome to the (Ironman) club! You've found a real gem, and at a good price, too.

You should be able to use a 14-28 freewheel, but you may need a new (longer) chain, and possibly a longer "B" screw on your rear derailleur to ensure the upper jockey pulley does not grind into the big cog. Do a forum search for "B" screw adjustment and you'll get some good info.

I say it's possible because I have a 1988 Nishiki that came with a 14-28 freewheel, and stock BioPace chainrings (53-42). The rear derailleur is an Exage Light Action (lower quality than your 600) and it handles the 28-tooth cog with ease.

If your area is really hilly, you might be better off getting a triple crankset.