Tourniquets are life saving, but don't buy cheap ones. There are a lot of Chinese knockoffs, which have been demonstrated to catastrophically fail when applied in Ukraine. The windlass tends to bend or break. I know there are a tonne of different tourniquets on the market, but for peace of mind I'd probably stick to the TCCC recommended ones.
Here's a list, although they do update it pretty regularly. There's a couple of Ukrainian locally developed ones now too which are pretty good, but for obvious reasons you'll rarely see them on the open market.
The other two crucial things to know are:
a) Only use a tourniquet when it's absolutely needed. That is for catastrophic haemorrhage. Think spurting blood from servered arteries, limb amputations etc. If you don't have this type of bleeding, try first to stop the bleeding with direct pressure, haemostatic gauze, pressure bandages etc.
b) Learn how to convert a tourniquet. That is to safely remove them, after putting in place other methods to stop the bleeding if possible. Tourniquets left in place for more than 2 - 3 hours can result in amputation of the limb, which is why point a) is so important.
If you're going to be carrying stuff like chest seals and splints (mentioned up thread), then you may as well extend to nasapharyngeal airway tubes and pulseometers.
In an emergency situation you have the following order of care:
1. Safety - is it safe for you to approach the patient? Think industrial accident with power tools still running (turn them off) or a cliff fall (don't put yourself at risk trying to climb down to them, unless you can find a safe route or have ropes etc)
2. Catastrophic haemorrhage - stop the bleeding.
3. Airway - are there obstructions to the patient's airway? This is where your airway tubes come in, before chest seals and way before splints. No oxygen will be the next thing to kill you, after loss of blood.
4. Breathing - is the patient breathing (assuming no airway obstruction). Now we're looking at sucking chest wounds.
5. Circulation - is CPR needed? Deal with other bleeds and burns, large bone fractures.
A pair of heavy duty medical shears is also going to be a good addition to your kit. Imagine a scenario where you're out hunting in winter and you have a catastrophic haemorrhage. No point applying a tourniquet over the top of three layers of clothes, and you also won't be able to accurately assess the bleeding through all those layers. Cut the clothes away.
Those £2 mylar space blankets aren't worth a pinch of poo, so don't bother with them for hypothermia. Buy a decent Blizzard survival insulated blanket. They're not that bulky and much more effective.
And get training! Basic first aid is fanastic, but if you want to take it to the next level, I'd recommend something like this:
College of Remote and Offshore Medicine, Remote Emergency Medical Technician course. It's 75 hours of online training, plus a full 6 days of face to face practical training in Malta. I've done it and highly recommend it (I also do a little consultancy work for CoROM, so I guess I would say that).
Edited to add: Chest seals are great and convenient, but be aware that if they're stored in a hot place, they'll turn to mush. It'll be almost impossible to remove the backing from the sticky bit. I've seen videos from last summer in Ukraine where this has happened. The medic threw away three seals in frustration before finding one that was usable. So, check where your seals are stored and/or replace them regularly. Also, in place of pre-packaged chest seals, cling film with the sides taped down with 100mph tape also works. The cling film will also be super handy as a burn dressing.