I think that shavings are best, my horse prefers them to sleep in. They are also cleaner, tidier and don't smell as bad. Shavings are specially designed for deep littering, so this makes your job easier and less time consuming. Though of course this doesn't mean you can't do a full muck out, as some people prefer to do this. Though once you start using them and try the different options you have with them you will soon be able to decide what you like best.
You don't have to take as much out of shavings as you do with straw, so in ways it is actually cheaper, depending on how messy your horse is and how often you do full muck outs, I would advise you do this at least once a week if you decide to only deep litter!
Summary of above:
Shavings are: Tidier, Cleaner, Less Smelly
They are less time consuming which makes your job quicker and easier
You have different options every day, whether you have time to full muck our or just skip out (deep litter)
They are supposedly more expensive but depending on how you use them and what you do, they can be a cheaper option.
As far as brands go I use Bedmax, which my horses seem to like. I have used them for a few years now and hey are really good.
I hope this was clear enough for you to understand, answered all your questions and was helpful. I have only mucked out wood pellets once before and in my opinion I prefer shavings.