The Fuse vs CB issue is an entire design philosphy discussion that could go on for days, be prepared. My boiled-down version: Fuses offer closer protection and higher interrupting capacity, but come with a risk of single phasing the motor, and you must keep spares on-hand to avoid costly downtime. Breakers open all 3 legs and can be reset, but need to be used in a coordinated system so that the motor starter breakers do not blow apart while waiting for some upstream device to clear a major fault. I personally prefer breakers.
Among breaker choices, MCPs (technically Magnetic-Only breakers, the term MCP is a brand name owned by Westinghouse and now Eaton) are typically used in motor starters because the Overload Relay that is already in there is relied upon for thermal tripping, leaving the breaker to short-circuit protection duty alone. The magnetic trip settings on MCPs are wider ranging than on regular thermal-mag breakers (typically), so they can help to avoid nuisance tripping on motor inrush current, which can be as high as 2000% FLA. The only problem with MCPs is that they are not UL listed for stand-alone use, they are only UL recognized (UR) for use in motor startes that have been SPECIFICALLY tested and listed as a unit by the manufacturer. So in other words, you cannot go out and buy an MCP and make your own starter unless you don't care about UL listing.
Thermal-mag breakers on the other hand are UL listed for stand-alone use, but because many designs have fixed magnetic trip settings, you may need to oversize the breaker in order to avoid tripping on motor starting. If however you are using a Soft starter or VFD, Thermal-mag breakers are fine since the inrush is limited by the starting device, and besides, you can't use an MCP on them anyway.
"Our virtues and our failings are inseparable, like force and matter. When they separate, man is no more."
Nikola Tesla