You mention familiy, so I will assume wife/partner and possibly kids.
Firstly - don't assume that any policies you currently have (ie life cover to protect mortgage) will cover you in the event of your death or injury whilst deployed. Many will have war exclusions, or a more specific exclusion of claims arising whilst on active military duty. If they are "silent" on the issue - ie don't appear to specifically include or exclude it - then it will depend on whether you declared your TA service when you applied. If you did, then your family would have a good chance of making a claim in the event you die, but would possibly have a bit of a fight on their hands. Dont' assume - ask. And get their answer in writing to avoid any squabbles later.
Second - there are a number of providers of forces specific policies. PAX (and RPAX), Service Life, Towergate, Forces Financial - they all have slight differences in terms and conditions, so make sure you check them all out carefully. Most importantly, check their conditions for on duty and off duty coverage. Forces Financial has a dramatically reduced benefit for on-duty accidents which makes it as much use as the proverbial tits on fish if you are buying it to protect you whilst deployed.
You should be looking to buy a bare minimum of accidental death and disability cover. This will, as the name suggests, pay you a lump sum according to the scale of benefits shown in the policy schedule in the event that you die or are dismembered/disabled due to an accident whilst the policy is in place. An IED strike or shooting is an accident - it is a sudden, specific, violent event, and fortuitious to the person insured. This means that it can be tied down to a particular time and place, isn't an illness or gradual deterioration and you didn't want it to happen to you! Don't underestimate the value of a payout for dismemberment or disability. Your wife may well have to give up work or reduce her hours to help look after you, childcare costs go up, paying someone to do the jobs you used to do etc etc etc. These all have a financial implication and a lump sum to help ease the process until everything settles down is worth having.
You can buy as much of it as you want to, up to the limit that any one provider is willing to offer. You can buy from more than one provider as you have an unlimited insurable interest in your own life. I will be buying as much as I can get across all providers when I go.
You can also buy life coverage (which includes death by natural causes, ie illness) - it is up to you whether you wish to spend the extra money to protect yourself against suddenly having a heart attack during the next 12 months. You can also buy critical illness cover which will pay a lump sum in the event of you being diagnosed with certain specified conditions - liver failure, heart attack etc. These vary greatly by policy, so again, read the small print. Same goes for private medical cover. For private medical, think of when you would actually get any benefit from it - you are really only considering post Selly Oak/Headley court. It can then add value with continuing ongoing treatment, reduced waiting times, guaranteed appointments. Worth considering, but if budget is an issue it would be nearly bottom of my priority list (just before critical illness) as the NHS, for all its faults, would still do the job - just not as comfortably.
Lots to think about - do some research, but if you have any questions, feel free to ask. I do not work for any of the companies mentioned, nor do I provide insurance to servicemen and will not give you specific advice as to what to purchase. I am not a registered advisor or broker. I am however a specialist insurance underwriter with lots of experience in this specific class of business, so have a pretty good idea what I am talking about!
There's plenty of info when you get mobilised. However I'd just add to the comprehensive advice above that RPAX is a bit cheaper than PAX, and if you take RPAX out before you get mobilised you can continue paying that rate throughout your deployment. Might be helpful if you're counting the ££.