Slims are more expensive due to the console price being more expensive. The slims are known to have far less problems with overheating. The different motherboards are basically improvements of previous versions.
I was lucky. All the boxes I opened for my Hunter were Desolate/Taken gear. On my 2nd Hunter I'm working on the Pariah Gear. I would have 4 Pieces but they were infused into my taken gear.
In order to run homebrew, you must have a special chip known as the RGH or Jtag hack. I suggest going to the 7s Homebrew Console Marketplace and find one there if you want to run games without buying them or flash your dvd drive.