IT is many fields. If you ask a careers teacher type person they will probably only point you at programming (which in and of itself is split several ways again).
Broadly speaking there are probably three fields, all take serious skills and lots of upkeep
Sysadmin
Systems architect
Programmer
Though any one should be able to muddle through the jobs of the other give or take some high level programming they are distinct enough that moving from one to the other might not be trivial.
Likewise there are related fields everywhere with the obvious one being electronics (programmable and embedded electronics systems that need programming are absolutely massive these days and is not going to go anywhere any time soon). There are more specialist things and field specific stuff if you want it like there are lots of medical tech jobs (all those nice expensive machines they look at your insides and fluids with -- they all have technical people either operating or servicing them).
Naturally there are ways of combining aspects of each like database admin and I expect I might get a comment along the lines of admin and architect are not necessarily different (true enough in a lot of companies but not universal to say nothing of the likes of programmers sometimes being tasked with making new things for the company to use). They are diverge a bit (network architecture, virtualisation and such like are big deals).
My usual advice was go down the maths path and pick either a maths place that has a computing course or an electronics place if you want to get into that a bit more as the other options are sketchy. This is not as true in the case of the latter part of that any more but get something with maths or electronics and it will still do you favours. I would still say do not force computing in high school scenarios as the first year of most university courses is going to say "forget what you know, here is how it really works". I am not really aware of any vocational paths into computing that I can wholeheartedly suggest, it is doable (the big two seem to be a small combo of distance learning, nightschool, do it yourself and gaining a few vendor qualifications and learn it and work your way in that way) but where in most other fields that have similar options for entry (the traditional manual trades and the like) I can reasonably say that if you work hard and get to know your stuff you will be able to use it I would not even consider saying that for IT.
On web design. Unless you are amazingly gifted at flash/html5 animation and/or artwork I would not suggest straight web programming as most do it now if you do not want to be back in school by the time you are 30. If you are going to be great at databases or great at programming and also being a web designer then maybe. If you are just using dreamweaver you are screwed and I am not to hopeful for the futures of "well I know a bit of php and SQL" types either.
I am getting close to starting to waffle and I am on a laptop with a keyboard I hate so I will leave it there for now. The short version is "there is much more to computing than programming despite what some might say" and "most of what I have seen taught at high school level might be nice if you aspirations are not to completely suck at MS office but not much beyond that".
