Let's pause for a minute or should we stop?

Pause has the laser ON and tracking the exact same spot forever.. (until you change it, anyway.) You can tell that for yourself, Leave a disc in 'pause' for twenty minutes, the take it out, the disc wil be hot, because it was still being constantly read by the laser all that time.
If you have the disc in the player, with the player 'on' but in stop mode, the disc will be a little warm, but not nearly as hot as pulled after pause mode.
The laser will last 100,000+ hours and usually fails from some other reason in the electronices tracking, or reading, rather than the laser itself dies.
So I personally would just go ahead and do what you like to do with pause.

Does it cause more stress on the transport to be spinning continuously as opposed to starting, stopping and then starting again?

Stress? for stopping starting and finding the spot again vs. leting it run in pause for any long time? Who knows for real. Someone might 'decide' they know, but I do not think any studies have been done on 'mean time to failure' comparing those issues.
When the unit is in pause, the tracking is in full use, thenlaser is reading, in order to hold the spot on the CD.
I just can't say anything about it.
Like when a flourecent light is left on it is better than turning it off if it is going to be used again within so much time. Same for a computer, better to leave on than turn off and back on within a hour.
But for a disc to stop or stay in pause.????
I mean yes leave it in pause if you have to answer the phone, or run to the restroom, Even to go eat dinner. .. but to leave it in pause overnight? ahhh no. Just my opinion.

If I'm going to be gone longer than the length of a song I generally push stop.