Since no one has said it yet, regarding the chimney, you have a choice of using the chimney or lining the chimney with a flue liner. The latter is generally preferable if you are installing a stove because (i) provided it is sized correctly it will ensure the correct draw from the stove to get the flue gases out of the chimney and a good burn rate in the stove and (ii) it is less faff than trying make a gas-seal on the register plate around the stove flue pipe. However, it can be reasonably expensive.
You'll need to remove the bricks from the fireplace opening to see what state your chimney is in. Make sure you check for a lintel and if there isn't one, you'll have to put one back in (we found ours had been removed as some point when a new throat plate had been added).
Once you have removed the bricks from the fireplace, have a look up the chimney with a torch and see if you can see any obstructions. If not, a smoke test will show up any gaps in the brickwork that will need fixing before you can burn anything in the fireplace (flue gases can be very dangerous i.e. CO poisoning, as well as the risk of chimney/house fire). You can buy a smoke test or you can ask a chimney sweep or stove installer to do it for you.
We found this site very helpful for information.
When a bit further on with knowing what you want to install, we found our Building Regs guy at the Council very helpful to nail down details of the hearth, clearances, flue etc. Inspection and certification cost us about £100.