Welcome
I took up cycling at about your age too. I think we are quite a common breed. It was a bit of a shock how much had changed since I were a nipper too! 'Cross bars' are call 'top tubes' now, apparently - I bet it's the yanks!
Best bit of advice I can give from my experience of buying bits of bike kit is not to economise. More than any other area of consumer goods you do seem to get what you pay for in cycling, or perhaps put the other way round - cheap stuff is more likely to be rubbish than a bargain and you spend more in the long run.
I think I'm going to contradict myself immediately though. You can buy an old fashioned conventional pump from Wilkinsons for £1.49 that works perfectly well as a get you home job. For home use get a stirrup pump to get tyres up to high pressure. Brands like Park Tools, Blackburn, Topeak and Specialised are all pretty good and spend around £25 or more. If you want a better pump to carry with you, look for the same brands, again you need to be looking at £25 or so, anything under a tenner will be a waste of money (but I hope someone on here will be able to contradict me). Blackburn's 'Airstick' I think is often recommended - will pump up to high pressures and keep working for a long time. They come in different lengths to fit the size of your bike frame. I've got a Blackburn mountain bike pump, which is fine. MTB pumps have shorter fatter barrels to shift more air into fat tyres, but don't usually get to such high pressures as the road bike ones. I still prefer using a conventional pump though and a firm called Zefal makes some good ones if you haven't got a Wilko's nearby.
Carrera bikes are good value for money and fine bikes.
Halfords staff & quality standards are variable though - hope you got a good one that was well set up!