The major two things on that list I still have to figure out are numbers 3 and 7.
(3)
Have you considered electric?
I use an IC3500 240V countertop induction plate, it's excellent for 5-6 gallon all grain batches. Takes 20 minutes to get 5 gallons of strike water to 175F.
I've done 10-11 gallon ones too, just takes twice as long to heat everything, but keeps the boil fine. I love that plate, and use it for many other cooking processes than just brewing beer. BTW, I'm brewing in the kitchen, the kitchen is mine, I'm the cook mostly. My wife is very fine with that.
For induction you do need a kettle that's induction capable, some stainless is, but not all. If a magnet sticks to the bottom it's induction capable. If it
doesn't stick it
may still be induction capable, but there's only one way to find out...
Triple ply bottoms help prevent scorching. But so does good stirring.
(7)
An immersion chiller (IC) coil is the simplest in any which way. Counterflow (CFC) is quicker, more efficient, and fairly easy to clean/sanitize, but it requires a pump.
Hydra's and such are IC, using multiple coils in one. They are almost on par with CFC, at about the same cost. You can have 20 oz of hops in your kettle, IC doesn't care. For anything that recirculates or has (narrow) passages such as some CFCs or homebrew class Plate Chillers you need some way to keep hops out of them. Either bagged hops or a hop basket, or some other way to keep them from exiting the kettle is mandatory. And a PITA.
You should brew a few times so you know much better what your needs are, equipment and space wise.
10 gallons is a perfect kettle size for 5-6 gallon all grain batches, but generally too small for most BIAB mashes, as it has to hold the grist
and all the water. A hybrid-BIAB process may work fine with that though.