Tents:
Don't get a single-skin tent (condensation). Cheap tents are OK in fine weather, but if you are unlucky with the wind you may have to decamp to a B+B or hotel.
Things to be wary of are doors that let the rain into the inner as you get in/out, and where the person at the back has to climb over the person at the door in order to get out in the night.
You should be able to get something fairly decent and not too heavy (2.5kg) for £75-£150.
Check out the Vango Tempest 200 or the Vaude Taurus 1
Stove:
A simple screw on to the top of the cylinder gas stove is simplest, such as the pocket rocket mentioned above (but there are plenty of alternatives). The ones where the gas is on the end of a hose do have some advantages (more stable, work better in the cold if have a preheat loop), but are heavier and cost more.
Avoid Camping Gas - the click-on stoves are only usable with blue camping gas cylinders, and the piercable ones have to be burnt right down before you can change the cylinder.
Gas tends to get slow at the end of a cylinder, especially if it's cold. With screw-on, you can swap to a fresh cylinder for heating and put the old one back for simmering.
I'd recommend these
clip on feet for the cylinders.
Sleeping
Mat: Wee Airic from Alpkit recommended. Use a spare jersey or something to keep your feet off the ground.
Bag: Compared to equivalent synthetic fill bags, down ones are lighter, pack smaller, more expensive, last longer, harder to clean
BUT down bags are useless if they get wet. To keep them dry, something like the Airlok XT drybags (from Alpkit) are recommended unless you use Ortlieb panniers.
If you go for down, the Alpkit sleeping bags are good value.