You need to back up a bit and firmly decide FOR WHAT PURPOSE you're restoring this bike. Do you intend to ride locally, with only moderate hills? Will you put on a rear rack and haul groceries or make day trips? Will you ride longer distances and explore? Do you want to begin training to ride faster and farther? The answers to these questions will help you decide which direction to go (at your present "fork" in the road between fixed/single and multi-speed). If you want the most versatility for speed, hauling, and terrain variations with the minimum of modifications, you'll probably want to keep it as a 10-speed. If, on the other hand, you want something to experiment on - with little intention of long training rides, climbing intense hills or hauling, you might enjoy a fixed gear bike. Fixed gear riding takes a certain level of (a) fitness and (b) bicycling skill. It's not for everyone and it's an expense for which you will recover your investment if you decide to immediately sell.

This thread began with a repair for resale angle. Now, you have too many angles to follow. You must decide and move efficiently in that direction.

For fixed/ss, you choose the crankset first, then specify the bb spindle length to give the appropriate chain line. Chainline is also specified by the spacing of the rear cog. So you'll have to have an idea of your wheelset and cog placement before buying the bb spindle, too. Exact placement of the front chainring can be varied by using the outer or inner flanges of the crank spider for mounting, and (to a lesser extent) by shimming the chainring from its mounting position (inward on inside position, typically).

Good luck. PG