all that is correct .
if you master is old you don't want to normally push the pedal more that normal sometimes you can mess it up
my two person system is
pump... slowly
pump... slowly
pump ...slowly
bleed
3 sets of 3 for each wheel starting from furthest from the master.
also be aware of the gravity bleed;
simply fill the master and crack open the bleeder and let it run for a little while .with the cap off.
most systems will gravity bleed this will also tell you that ya dont have a swelled brake hose or a smashed or kinked pipe
PAY ATTENTION not to let you master run dry either way you choose
I have the might vac too its the cats meow reclaims the old fluid and dosen't make a mess especially if you have painted stuff around worth the investment
P S brake fluid wears out (get dirty) too so if you periodically bleed your system every year or two it will prolong the system
SR66