I'd recommend an inner diameter 75-100 mm larger than the outer diameter of the crucible. Any narrower and you can't drop charcoal briquets (If you use them) down around both sides of the crucible -- and also proper lift out tongs are sometimes pretty thick, and hardly fit around the crucible on both sides before they are clamped down. Particularly if the crucible tilts against a wall -- as my last pour demonstrated. Also you may at some point want to go to a larger crucible.
I just built my last furnace 7" dia, and I wish it had been 8" (200mm) as my first furnace had been, for all of the above reasons.
I think 200-225 mm bore is a good diameter for small furnaces in general.
The only problem with that might be whether you have enough room for refractory with whatever metal shell you are using.
I used 4" (200 mm) of refractory for an iron melting furnace using traditional materials (clay sand brick).
My first aluminum furnace had a shell of only 1.25" (32mm) (clay/sand) and it was perfectly fine for aluminum, and could handle an occasional brass melt.
