There are Citylink coaches that can take you from Portree to either Fort William (and onwards to Glasgow) or Inverness. Citylink Advance reservations are recommended as there are not many coaches each day and they get very busy. The bus drivers are not renowned for their soft skills, so if you don't have a ticket and the bus is full you won't be getting on board.
The coach also stops in Kyle of Lochalsh from where you could pick up a train to Inverness National Rail
- although if you're already on the coach there's not a lot of point in changing to the train! There are no rail lines on Skye.
Yes you need actual hiking boots if you are hill walking in the Highlands. You will also want to have waterproof over trousers and a waterproof and windproof shell jacket, plus gloves and hat. You will also need good maps (Ordnance Survey OS Explorer series) and preferably a compass. Either paper copy or downloaded to your phone. Don't rely on a good phone signal in remote areas.
Hope that helps
Jacqui (Skyegirl)