This is all just a personal opinion so guaranteed people will think differently but, for a beginner who doesn't want to spend a lot in case they don't enjoy it and would be carrying everything in a rucksack (car-camping isn't camping
) -
Tent - A basic 2 man dome tent that is waterproof, has a liner (so the condensation doesn't drip on you as you sleep) and has a ground sheet built in is around £50 and should come with everything you need to pitch it except a hammer/mallet depending on the ground but it's always a good idea to get more pegs just incase.
Sleeping bag - A 2-3 season bag (ideal for everything except frozen winters) is about £50 too. There's two main designs - "mummy" has a narrow foot end so there's less air around your legs to get cold whilst "square" is wider at the feet and can be opened to become a duvet. I prefer square, most bags are however Mummy shape - try one of each before buying.
Mattress - My choice is yes but at the very least get a thermally shielded rollmat (£10) for comfort to start with. I use a self-inflating mat which is an air mattress but only 1-3in thick rather than a big chunky one as it means I can roll it up smaller and it's very light so it's easy to carry around and an OK one is about £30-40 (also get an inflatable/fleece pillow).
Again, opinions will vary a lot, as will the costs. Have a look in your nearest Go-Outdoors as I don't think there's many camping shops around any more like Millets/Blacks etc to see what they have for starters.
My personal setup is about £500 and isn't even that expensive compared to some stuff. I use a lot of Snugpak stuff, their tents, sleeping bags etc and an Exped Downmat 7 Mat.