Reading between the lines, if you are shooting Pheasants, Pigeon and Duck with a Shotgun, and want a .22 for rabbits, presumably you already have access to land?
All you need is written permission to use a .22 there, and then toddle to the Police Station for an FAC Application. It is broadly the same as for SGC, however, you will need to specify what type of rifles to wish to acquire, and for what reason, e.g.
.22 Semi auto (or bolt action) for vermin control on xxx (named land)
Remember, if you want a moderator, you will need to ask for that as well, as its a licenceable item.
You will also have to specify how much ammo you need to buy and hold. .22 ammo is not expensive, and think about how convenient it is for you to get to a gunshop to buy some, and how much you will use. I have buy 1000 and hold 1200. (It can be cheaper to buy it in 500 or 1000 round blocks, but most FEOs won't accept this as a valid reason) You will also need to specify that you want expanding ammo for vermin.
Your ammo, unlike shotgun ammo, will need to be kept in a seperate safe. The likes of B&Q do small valuables safe's for between £20-£50. Get the biggest you can afford, as if you end up with several different rifles you might have to store a fair bit of ammo.
You can keep the rifle(s) in your shotgun safe, provided you do not share it with anyone else (e.g. your dad) if you do, you might need another safe for your rifles, or at least to secure your rifles within the safe so only you can take them out, with a cable lock, for example.
Deer stalking is a different ball game, and your route in depends, to a great extent, how flush you are and where you live.
If the land you shoot on already has Deer present, then obtain permission to stalk from the landowner. You will then need to learn to stalk. The most effective way of doing this is to go stalking with a proffessional. This does not have to be expensive; look in the back of Sporting Rifle Magazine for loads of adverts. Obviously, try to pick someone local to you who offers stalking on the same species as are present on your land.
You can also do your DSC 1 exam/course, which can help you secure land etc. However, it is a purely theoretical course, and you will probably learn more with a stalker in the field than in a classroom.

The Police may try to insist you do DSC 1 before they let you have a stalking rifle, they tried with me. This isn't strictly legal, and if you are a member of BASC they can help. I've successfuly fought it, so pm me if you want advice on it.
If you do not have deer on your land, and (for the foreseeable future at least) only intend to stalk on a 'pay-per-day' basis, then its easier. Simply book a stalk for next Autumn/winter, and ask for a confirmatory letter for the Police. Companies will be quite used to this. Fill in your application asking for a suitable stalking rifle, for shooting Deer, and specify as a paying client, rather than on farm x or y.
If Tunbridge Wells is within your orbit, I can pm you the contact details of some excellent stalking there with a very friendly pro.
Defence Deer Management is not open to Territorials, but is to Regulars. I am in the same situation as you and have already enquired. PM me for further details.