A question about headphones

I've decided I would like to give the headphone experience a try because I am an early morning person and I would like my wife to enjoy her sleep.  She is definitely not an early bird.

I have a McIntosh C48 preamp and it has a headphone jack on front.  I have plugged my BT transmitter into this and paired with my Bose noise -cancelling headphones but can't say its anything to write home about.  Do I need a headphone amplifier and where do I connect the amplifier to my rig?

I like headphones that fully encapsulate my ear.  I can't see that open-back headphones appeal to me.  I am about 20' away from my rig and although I would consider a cable, what's the consensus on BT headphones or a combo BT / cabled?

I live in Canada and I was thinking to make a start, I would not want to sink more that $500 into headphones until I am convinced this is the route to go.  I still don't know about the headphone amp and its cost - if I need it.

I don't post much here but I follow this forum daily ad appreciate all opinions and feedback.  Thanks in advance everyone.