Those tires should work fine. If you start having lots of flats you can upgrade. If the fit doesn't seem perfect you could try some different stems and handlebars and that might dial it in alot better. A shorter stem or a swept back bar might make the bike fit a whole lot better.

Post up some pics of the bike. Some people repaint bikes, but I kinda like the vintage look. Alot of times cleaning up the frame and using some wax on the paint can really shine up an old bike. If you want to touch up a couple spots get some cheap nail polish (I would just take the bike into the drugstore Walgreens etc with the best selection) and this can really work wonders for the look as well. Having a bike that has some general ugliness makes it less liekly to get stolen and you don't have to worry about it getting scratched up if you lock it up somewhere.