Welcome to the community
First off if not currently using LMCE then it would be a good idea to get a box up and running just to play with. You are very lucky you will be the only one living in the house as many of us have to build systems while living with SWMBO and constantly face the firing squad
Probably most important thing is to make sure you get Nvidia cards and 2 nics in the core or else you will have issues before you even start. Also bear in mind that 810 does not support some of the newer hardware althought I'm not sure to what extent.
Some things will depend on what level of renovating you are doing such as automation would be either KNX or Z-Wave (there are others but these 2 seem to be pref technologies at the moment). KNX requires rewire and z-wave just gets attached to existing switches.
I use HDHomerun for TV and has always run well compared to PCI cards I've used plus does not takeup space in the core. For storage some use NAS and others such as myself have storage in the core.
Cat6-7 probably a better option as cost difference over 5e is minimal and it does give a little bit more 'future proofing'.
As for what order to do things its really up to what you want working first. Get a core up and running first with some media on it made sure all working well and then image often so that if/when something breaks it is easy to roll back.
Check out wiki and http://lmcecompatible.com/
for hardware that works and then ask specific questions once start getting a list made.