While I cannot say definitively what is "Best", I can give you some certain answers...
Category 6 cabling for the most part offers some performance / reliability improvements over category 5e, it will carry 10GbaseT to a limited extent, but it too is limited. I personally tend to be cost conscious, and upgrading from 5e to 6 was I felt worth the extra cost.
Generally solid wire is used in wall, stranded used as jumpers, however I have found in actual use, that solid works very well in both applications.
Yes, you want to use copper.
The 802.11ac WiFi standard is still in Draft status, meaning that at any time the standards body can make any changes they see fit, and you may, or may not be stuck with incompatible hardware. I would steer clear of ac for a while yet.
In practical application N300 is the fastest you will see commonly implemented on devices, although there are some N450, N600, and N900 out there. Out of all of my WiFi devices, I have ONE that goes as far as N600, and it is an add in WiFi adapter for my laptop. Everything else does N300. So chances are going with anything much faster is really going to be a waste of money and likely to be incompatible in the future if you are talking AC.