The LED recessed lighting thread which started with Kitchens has more answers

1. Most commonly used lighting will be run off line voltage (120V AC in continental USA).
With the push towards greater efficiency, incandescent lighting is on the way out.

Halogens will never achieve the efficiency of either CFL or LEDs. LEDs today can closely mimic the light color of halogen (~3200 - 3500k) without any UV output (halogen bulbs could produce UV light).

Switching to line voltage halogen lighting will require that the recessed cans are properly insulated so that the heat generated by the bulbs will not create a fire hazard.
2. A CR4 has a power requirement of ~ 9.5 watts, so, it is possible to put 14 on one circuit.

There are good reasons to split the lights between different dimmers -
a. zones/ layers of light (assuming 1 massive room).
b. a typical residence will not have a massive space requiring 14 lights to come on at once.

3. Remodel housing is supported by the ceiling board alone and intended for fixes after the fact.

Since you're doing a gut and rebuild, it makes more sense to use new construction housing since you'd be able to place the cans where you want before the sheetrock is installed.

Here is a link that might be useful: LED recessed lighting

Thanks so much, incredibly helpful. I didn't know halogens needed insulation.

Sounds like we should just commit to LEDs, but with stand alone housing, we'll have the flexibility to make changes without having to pull the housing out of the ceiling.

Really, really appreciated.

Halogen lights run hotter than incandescent lights. As such, the housing immediately over the lamp needs to be kept away from direct contact with potentially flammable material (e.g. - cellulose, cotton, ...)

Most cans today are rated for direct insulation contact. There is also a thermal cutoff circuit which will switch off the power at the can when a temperature threshold is reached.

If you look at the 4" cans @ Home Depot which are also used for halogen lamps, the construction ensures that there is a significant air gap - there is a aluminum box on the outside so that the entire assembly can be buried under insulation (cellulose, fiberglass batts, ...).
http://www.homedepot.com/p/Halo-Air-Tite-4-in-Aluminum-Recessed-Housing-H99ICAT/100186076

The second example is that of a can that is for non-insulation contact
http://www.homedepot.com/p/Halo-4-in-Aluminum-Non-Insulation-Contact-New-Construction-Housing-H99TAT/100066352