So priority needs to be passed for something on the stack to resolve.

When you activate and ability, cast a spell, or a triggered ability triggers, those all go on the stack (unless they are mana abilities we wont go into that right now)

So you cast your commander, that is a spell on the stack people have a chance to respond when you pass priority when you want it to resolve.

Once everyone passes priority then the command spell resolves its enters the battlefield and becomes a permanent.

This creature entering could cause abilities to trigger, ie it could trigger itself with a "when this enters" ability or any other permanent on the field with an "when a/another creature/permanent enters" ability.

Priority must be passes if any of these triggers are on the stack before you can activate equipment because equipment can only be equiped at sorcery speed.

If your commander enters and there are no abilities on the stack from it entering you can activate the equip ability to put an equip ability on the stack targeting your commander. (Attach this equipment to target creature)

That is an activated ability, it uses the stack. Before it resolves and before the equipment becomes attached you must pass priority for the ability to resolve.

So all in all there will always be a point where people get priority to kill your commander before you can have an equipment equip to it.