Most people would start this by visiting a "stoves" shop, they always
have a resident expert and good local contacts into other trades.

They will probably be keen to take the "whole job" and contract out
the masonry work. Least hassle for you, but probably the highest price
if you go with them. But why not find out what they recommend and then
talk to some other local contractors independently - you can always go
back to the stoves shop for the install, if you want to give them some
business.

You don't say if you're on a tight budget or looking for the rolls
royce solution. I've recently had an (oil-fired) Rayburn installed,
and used their recommended contractor (in North Norfolk). Whilst he
wasn't cheap, he had a very "get on with it" attitude. His standard of
work was faultless. Aga-Rayburn also do solid fuel Coalbrookdale
stoves (and I mean stoves, rater than the ranges they're famous for).

However I did my woodburner (a Jotul - recommended) myself, bought the
stove and liner online (where they are significantly cheaper), built
my own constructional hearth etc. There is a lot of money to be saved
this way.

Finally - another obvious starting point - talk to your local planning
dept. Your project might have to grind to an early halt if they're not
keen.