One point to note is carpets come in "roll width", 3m, 4m, 5m etc. So with an odd shaped room you can end up paying a lot for unused carpet. So what calculates out by area as say =A31378 can end up being =A31742, quite a jump.
It can be worth checking around the more specialised trade outlets not in "retail areas" re business rate, staff & so on overheads. You can often pick up your size of carpet at a good price. For example I found another =A350/yd carpet in remnant form at =A322/yd - a popular "neutral with pattern" too which tend to go for quite a bit more.
Underlay can be bought cheaply online, 9mm bonded-foam is good for downstairs, 11mm for upstairs (can be a bit too bouncy & make tables wobble downstairs). Tredaire Dreamwalk & Cloud 9 are common brands, half rolls about =A320 delivered, full rolls about =A345 delivered (15 metres square) and some places doing full rolls also sell by the square metre so you can pick up an extra few metre-square if need be without buying units of full rolls. The foam insulations are about
2.5-3.0 Tog, waffle rubber about 1.2-1.6 Tog, rubber crumb about
1.5-1.7 Tog. I'm still not convinced the foam underlay will not tread down over time (PU foam suffers about 30% static set eventually and a carpet can be heavy in itself) however it is starting out thick so it may hold up ok.
Next is what mix, eg, 100% polypropylene to 60/40 80/20 etc wool/ synthetic mix. A very high wool content combined with lightweight can result in a carpet that goes to hessian relatively quickly in a bedroom where movement is "along tracks" and pedestal chairs go over it. Choose carefully. If you have badly cupped floorboards likewise consider hardboard over the top then an underlay, because cupping can break the back of a carpet in a line over years. No idea if most people change their carpets every 5yrs, but relatives get 25yrs+ and the older heckmanwick (spelt wrong) can go 60yrs in hotel grade on high traffic areas with no hessian showing or "tracks".
Finally, if measuring yourself, always measure into the door reveal. You would be amazed how many people don't and then need to get the carpet machine jointed "behind the sofa, behind the bed" or such like.
If you have sockets on skirting fed via cables from below, make sure the fitters slot the carpet and fold into place - not hack great "laybys" out of it so when you move the sockets up you aren't left with a remedial carpet cut-n-fill job that is actually rather difficult to get perfect. Saw it happen at a private dentists, needed new carpet throughout courtesy of their slapdash. If any services or such like exit/enter the floor and may be moved, get them to cut & fold under so you can at least avoid patching later.
Asphalt & carpet grippers. Do not let them nail it, bond it (gripfill and the like). Nailing it breaks up what may be your only damp course (and it does quite well, along with driving levelling compound buyers insane).