We used the Which? mortgage service and were very happy with them.
They are salaried and not on commission, any cut goes back to run the company - so it's as impartial as you could really get.
We could either pay them a set fee (£1000 I think), and then we would be paid what would be their cut (typically a certain percentage) when the mortgage was setup, or just let them have their cut and pay no extra up front.
It worked out better to let them just take their cut, and the guy even advised us that was the better option.
I would definitely advise using a broker, I don't know that I'd trust a banks own mortgage adviser to not be incentivised in some way to offer their own deals over another's - so you won't know if you're getting the best deal for you.
You're in a very strong position with nearly a third of the value as a deposit so you should be getting some really good deals. We had £90K deposit on a £290K mortgage and got 3.09% fixed for 5 years with Nationwide.
I personally think fixed rate is the way to go, and for as long as you can get it. Interest rates can't go any lower, so a tracker can only ever mean you pay more a month rather than less.