when to start jr pass?

hi all,

my apologies if similar questions have already been asked, but i just want to make sure i have the right information!

we will be in japan for ~12 days, landing at narita and then spending 5 nights in the shinagawa area, followed by a night in hakone, 3 nights in kyoto with a day trip to nara, 1 night in hiroshima/miyajima, and 1 night in osaka.

we were thinking of doing a 7-day jr pass and activating it towards the end of our stay in tokyo, but i want to make sure that won't hinder our travel around tokyo from our base in shinagawa. we are staying very close to the jr station there, but do i understand correctly that we can/should use suica or pasmo for the metro and on the jr yamanote? or would the jr pass be of benefit to us in tokyo based on our location?

does it make sense to pay for the n'ex out of pocket, do suica or pasmo (is one better?) to get around tokyo, and then activate the jr pass for our longer trips?

thanks in advance for any helpful advice!!