Thinking about replacing old fuse box. Looking for advice
Your fuse box is a sub because the “switch” is the main. (From Beal) Installing a sub service panel is a bigger job, but if you've installed new boxes before the principles are the same. Read the section in the code, and leave yourself enough space. Remember you need a separate circuit for the light above the panel.
I would recommend you install at least a 20 breaker box. A box with more spaces costs only a little more, and it's astonishing how fast you use them up.
(If you don't already know you must turn the power OFF to work on it, get an electrician!)
Your best friend on this is the free online National electrical code at NFPA.org

Just by the way, the fuse panel you're replacing is an old Federal Pacific box. If you have other Federal Pacific boxes with Federal Pacific BREAKERS, run, do not walk, to replace those panels!!
FPE Stab-Lok Electric Panels Don't Need to be Inspected; They Need to be Replaced!
The problem with FPE Stab-Lok breakers is they don't trip when there's an overcurrent, and the breakers themselves have bad connections inside that can start fires in the service panel. The problem is particularly bad with tied double gang breakers- these ALMOST NEVER TRIP FOR AN OVERCURRENT!!
There are no safe replacement Federal Pacific breakers. The Federal Pacific box itself is defective. You have to replace the whole thing.
FPE Stab-Lok Electric Panels Don't Need to be Inspected; They Need to be Replaced!