New bottom bracket and crankset - what spindle length?
Chainline is important, more so for modern 10+ speed systems. A six speed system is more forgiving of misalignment than one would guess. Since both BB are square taper all you need to do is remove it and see what the size is on the BB itself. The shaft will only allow a crank on so far (that's why its taper). By buying the size currently in the bike you should come pretty close. You'll see plenty of cross chaining with modern bikes and they survive. Although not the same exactly, I think you'd be OK as well.

(Not so cheap but) Simple Solution:
Why not just replace the chainring if it is that worn? Much easier to do, and much cheaper. Also, if your chainring is in that bad of shape it is likely your freewheel is damaged too, as is the chain. You'd be better served by replacing the drivetrain entirely. Removing freewheels are not as easy as hubs, but it can be done. You'll have the ride you wanted without the compromised components causing mischief and making you think it is a chainline issue.

Good Luck!