Manicure tools must be washed after use and let to dry. If you put a wet tool in a box, it may get rusty, even if it’s made of stainless steel.
Get a wall kitchen magnet for knifes and screw it in you bathroom. Put all the manicure tools on it. That’s the best way to store the tools and have them readily at hand at the same time.
Please note, that not all metals are magnetic. For instance, titanium and aluminium, won’t stick to magnets, so you may want to attach a steel keyring to hold them on the magnet. However, most manicure tools are made of stainless steel, which is highly magnetic.