I have to say this is a topic that is close to my heart and this is always my advice to potential newbie stalkers.
To get into stalking first and foremost before you even buy a rifle or apply for a firearms certificate you need land. Land is the hardest to come by so a plan of what you are wanting to do and how your going to achieve it is good specially before you apply for your FAC as that is the main question you are asked.
Bare in mind and FAC application can, in some cases, take over a year to get so giving you lots of time to sort things out or change your mind but in the end it is the hardest part of the process and am afraid depending on how passionate you want to get into shooting can be the most stressful part of the whole shooting experience. While you are in the application process though spend time getting to know the community and making contacts as this will only help, just one thing to remember if your planning on stalking as your main shooting hobby to make the most of it you need to apply for a calibre over .243. Reasons many on here obviously know about and not going to get into that just now.
Ok so you have your certificate approved with your chosen calibre what should you do now?
Firstly set your self a budget and as it is (possibly) your first rifle don't go all out out and stick to what you can afford.
The industry is awash with second hand rifles as you will come to learn that like any hobby the guys who like to spend will spend regularly and change their equipment regularly so take advantage of it. Cheap is not always bad in the shooting world and there is a lot of top quality second hand products available and old also I have to add is not a bad thing either.
Rifles - whatever calibre you have been approved for a good centrefire package can be as low as £250 , as long as everything looks good no rust or damage to the crown and that it shoot straight then you are off to a good start. Now if your buying new it is worth getting advice but you can get brand new rifles for as low as £450 for instance at the moment you can pick up a brand new Browning Abolt 2 for around £450,
Just remember watch out for brands though that require modification to get them to shoot good such as Howa, Their standard Hogue stocks cannot be used with a bipod as the stocks are too flexible and certain years of the 1500 series have bad barrel material, so do your research, but having to spend another £200+ on a stock for a new rifle defeats the purpose of sticking to a budget.
Scopes - Scopes are a minefield and I spend a lot of time reviewing scopes. The best stalking scopes on the market are still the fixed power ones. Second hand you can get an excellent stalking scope for around £250 such as a Meopta 7x50 or Doctor, new the Schmidt and Bender 8x56 are arguably the best stalking scope on the market, but, the choices are endless. Just remember shop around. When looking for a stalking scope you need something robust lightweight and not too complicated. For stalking I always advise to stay away from your target brands. You will see social media promoting what looks to be a good deal for brands such as Hawke and Nikko Sterling but these type of scopes really are not well placed for stalking due to their construction, so what your looking for is a good metal tubed scope that is going to put up with the crap of a long "back slap" and the terrain you through at it and this is one of this is one of the reasons why fixed power for the novice is genuinely better than variable zoom scopes.
If your interested ONLY in variable zoomed scopes then you have a to wade through the minefield of focal planes and reticles, I would advice to get to know what you got and stick with it until your ready to progress.
Binoculars - right here is where I am going to sound like a hypocrite. I review some of the best binos on the market and I constantly show products that are phenomenal high end glass but no matter how much I would love to own them I cannot afford them, under contrary to belief and although I stalk a lot and I am very prominent in the stalking industry I make less than £15k a year through stalking so I cannot afford highend binos. I use a pair of Barr & Stroud Sahara 10x50 binos and they cost me new £77 plus postage from Ebay around 4 years ago and these are my day to day binos and they are very good and do me perfect. I have left them on the hill and went back and found them, I have used them in the best and worst conditions and they work daily for me and most of all if I break or lose them I wont be heartbroken if I have to buy another pair.
Moderators- Get what suits your rifle even the cheapest ones work well.
Clothing - WOW this is a real bee in my bonnet ------ DO NOT PAY £400 for a pair of trousers that you are going to wear once a month or a couple of times a year, stalking is not a bloody fashion contest you do not need £400 jackets and trousers to get the job done, I have shot deer in jeans and trainers as well as full camo gear or tweeds, wear what is comfortable and that does not need to be expensive. Bare in mind you may come across a lot of rip hazard such as barbed wire fence and crawling through bracken and heather, rough terrain is not sympathetic to your pocket so you should be. Trust me I drag deer in conditions as low as -15 in £30 trousers and a £40 jacket with some baselayers.
Boots - Invest in a good pair , Haix and Military surplus are good and very cheap, some of the big brands are awful such as Harkilla , I use Bestard and out of all the 5 big brands I have used I find the Bestard Explorers the best and at £200 for me it is worth the investment every 4 or 5 years.
Anyways I have a school run to do now and I been sitting here for the last five minutes typeing this out and I am running out of things to say. What I have been getting at is that do not spend a fortune in shooting at the start off, shooting is a lifestyle choice and like any lifestyle it progresses as you grow. I shot my first Royal with a 30 year old Parkerhale at the age of 13 and I shot a 20 year old RWS 22-250 as my first centrefire rifle, my first .22 was an ancient BRNO . on my first year of professional deer management after a long break from shooting I bought a Browning Abolt 2 Package in .270 that cost £950 which was rifle, moderator and Kahles 6x42 scope before upgrading to my current Tikka .270 I shot well over 500 deer with that old rifle and it still is used by another stalker as we speak and with that 6x42 Kales Helia scope my longest kill was a hind at 483yrds.
So remember stalking does not need to be lifenchanging expensive.