Let me start off by saying I'm a long time lurker and have finally decide to join.

I have this 1986 Bridgestone 500
A year ago a fell on top of it and severely bent the front wheel.
To me that was enough of an excuse to make some upgrades.
I found a donor bike that I took some tricolor bits off of and sold the rest to break even

With the upgrade I went from a 6 speed freewheel to a 7 speed freehub.
When I'm on the smallest gear the chain rubs on the outer chain ring.
I wanted to get a new bottom bracket
I checked Sheldon Brown's info for lengths
According to the info the 6400 had a 113mm spindle
Can I just buy same size bottom bracket and ride away
Or is there other factors.

I only ask because I read older posts that said the bottom bracket length is determined by the crank used

I have a shimano 600 6207 crank by the way.

Sorry if this is an obvious answer but I've never worked on bottom brackets before