Wow, Stephen. Welcome to camping! I am sure that you will not regret it, and that your sister will love it. These are just a few random thoughts that have immediately sprung into my head...........
Get out there and do it for yourself....you will learn to do so much so quickly. Don't be afraid if it goes wrong, as campers all tend to be extremely friendly people and there will never be any shortage of people to help or offer advice. Every one of those people were novice campers once.
You will be wanting to get yourself equipment on an on-going basis: each time you go on a trip you will want to get yourself another bit of kit: don't try to buy it all at once: that is impossible unless you have bottomless pockets! The way I justify buying kit is by looking at the little amount of money it takes to stay a night at a campsite: if you were staying in a hotel it would cost £60 more per night. I will then buy one or two things with that in mind and then the feelings of guilt aren't so strong!
I also suggest buying the best you can afford as the majority of decent camping equipment, if treated right, will last a very long time. I'm still using equipmnent that is over ten years old. Saying that though, the likes of Argos and Halfords can sell some decent stuff at decent prices. You can also get good stuff from the likes of Blacks or Millets. Shop around, especially as it is the end of season (believe it or not) for many of these bigger chains and they now need to move stock. If you do buy something in the end-of-season sale, open it up and test it out, even if you are not going to use it until next year. Last year we bought a brand new Outwell Hartford (funny enough!) for half price. We didn't put it up until six months later, only to find it had no poles!! We are now dancing though hoops like nobody's business to try to get this resolved but it would have been so much easier to sort out in October.
You will also want to consider how much space you will have in the car: that Outwell tent will likely take up the whole boot of all but the largest cars, so be sensible and pack wisely. Don't forget that, as well as your camping kit, you will also need to pack stuff to wear: how are you going to pack it all into the car? How many people need to go in the car: can you use the back seats or do you need to look into roof bars and a roof box, or even a trailor?
Each time you go on a trip have a look at what other people do and how they do it. After 12 years I am still picking things up from people and learning to do things slighly differently or better.
Before you go find yourself a decent camping store that does camping and nothing else. Argos, Tescos and Blacks are good up to a point, but you are likely to find that they are quite limited on the accessories-front while the specialist will have everything and anything that you mght ever think you will need (and a whole lot more that you will never need). You are also likely to find that they are very competitive on the price front too. Pick yourself up a decent rubber mallet as these are the best for getting your pegs into the ground and about a dozen or so decent, hefty pegs: it is not believable how many pegs you will go though.... but not if they are a decent thickness.
You will then want to get yourself a decent blow-up mattress: there is nothing worse than camping for a week or so and not getting a wink of sleep because you are so uncomfortable. For this reason avoid the cheapest and fork out a little. Decent sleeping bags are a must if you are planning to camp in the UK or Northern Europe. If you plan to go to hotter climes then normal bedding and sheets will do. A pump of some kind (preferably battery operated) is also essential to inflate the mattresses. Avoid those little foot-pumps as they take forever, in which time every person in the campsite will have fallen out with you because of the noise they make.
You will then want to look at somewhere to sit. Sitting on the floor is fine, but the fishing-type chairs are so much better (and to be honest the ones from Tesco will probably do OK to start, although you will probably want to buy better later). A few years down the line you will want to look around for a decent table.
If you are only going away for a few days at a time you will probably get away without a cooker, provided there is a good pub nearby which does good food or a selection of restaurants. Always do your research if you do: the campsite reviews elsewhere on this website are great to help with this: most reviewers tend to mention the proximity of the pub and other restaurants, etc., while some sites may even have a decent eatery onsite. If you are going away for longer periods of time they you are going to need to get a cooker: make sure it has AT LEAST two rings - one for the pasta for other for cooking meat, heating sauce, etc. You cannot do this on those wee one ring things that attach to the gas bottle. You will also need to get a gas cylinder and here there are choices. You are best to go for Calor gas or Campingaz. Both do cylinders of differing sizes and both are initially very expensive (as you have to buy the cylinder itself), although they are more cost effective over time as in future you just swap your empty cylinder for a full one. I don't quite remember the cost of swapping as I haven't had to change my campingaz cylnider in a few years (see - cost effective), but I expect it is about £20. There is also the option of buying disposable gas bottles. With these you avoid the bigger up-front costs, but they are expensive over the longer term. I would advise you to talk to your specialist camping store on this one, as they will be able to advise you on what equipment goes with what cylinder and what regulator you will need.