Welcome to the forums!
my 2 cents on your conundrum: Get a cheap fixie to go around town and spend some time and effort on upgrading that Chris Chance to specs more to your current need. I'd suggest a period correct wheelbuild and a cassette with a wider range, and possibly a triple. This is a very short and condensed answer, but we're here to answer all your questions in detail
and feel free to post some pics as well!