Illustrator could be good for sketches only or pictures a'la "animated movie". For the rest I would still suggest PS (or Corel Painter, but I didnt use it much so cant recommend).

Here's how I would do it. Attachment related. I don't know how knight helms work, and just made a quick google image search for one to try and figure stuff out. I assume you can turn your head while wearing one and it's not like... bolted to the neck piece, so it's just headgear. Do just about all the drawing lightly so it's easy to erase:
-draw a potato-like shape to represent the a head, then draw a horizontalish line on it somewhere around the middle height to mark the would be eyes, then draw some sort of line or j to represent where the nose would be, to make it easier to feel your perspective or something
-draw a basic shape of how you would imagine a head covering metal pot to look on the head. just think of stuff like "it can't cover the eyes, if it goes over the nose, it needs to bend outwards a bit to make room for it, it can't be smaller than the head". if you're crazy enough, take an actual potato and wrap some paper on it or something (or be boring and use a mirror and a real head) :p
-pick a spot for the screw or whatever that attaches the face guard thing, it feels to me like it makes sense for it to be a bit high, like somewhere above the ears
-this one's purely optional but I feel like it helps: draw the face guard on the face to get an idea of the size and shape (needs to be large enough to leave room for the nose or something)
-now draw the face guard in the up position. the earlier step helps
-try to pick the important lines, and draw them with more force, and possibly start adding missing details like the area that's behind the head potato
-erase the lightly drawn lines, and redraw the harder drawn lines if they got erased as well. add details that seem to be missing.
-add decorative stuff if you need any, and never ever copy/imitate my shading, it's bad

Vector art is a whole other beast. I don't know what Illustrator's support for pen input is like now, but stuff like shading is easier in raster-based editors (Photoshop).

I suggest Photoshop or GIMP . . =)

I'd start out by drawing by hand in pencil and scanning it in to colour it. Photoshop is very good, yes. But it depends on what kind of look you're going for. Corel Painter is fantastic and used by a lot of game concept artists. In fact, on that note, when you've got the basics down and want some pro advice on how to take it further check out: http://www.conceptart.org/
It's a forum for professional concept artists. They're usually very helpful to those looking to learn.

I'd recommend investing in a graphics tablet at some point. But make sure it's something you're going to get a lot of use out of first as it's quite the investment.

I would suggest pencil/pen and paper for practice. I guess I'm a little biased because that's how I started. I'm no art teacher, but it seems like keeping the interface between the image in your head and the result as simple as possible would be better for learning.

I do recommend reading a book to get you started. "Drawing on the Right Side of the Brain" by Betty Edwards helped me a lot. It's a very easy read and aimed at a total beginner. One of the most important things it teaches is that the analytical thinking part of the brain is what keeps most people from drawing well. You have to try to stop classifying and thinking about the things you draw in terms of what they do. Instead, just try to see them as lines, angles, shapes etc. When you draw a portrait, try to directly reproduce what you see without interpreting things as a nose, a mouth and so on. This is key because as a child you probably learned to draw a mouth like a simple curved line. If you want to progress beyond drawing like a child you have to erase all these things from your mind and try to see things as they really are (lines, angles etc.) instead of seeing mouth shapes, nose shapes and so on.

I will try your method tommorow, thanks.

Well if I would buy just one book about drawing is this the one I should buy? The best of all? :) If yes then I will soon head to bookstore and buy it.

I would a bit more tentatively recommend Drawing on the Right side of the Brain. It has some helpful tips for very beginners but it has limited use and I find it’s easy to grow out of relatively quickly. For instance I assume one of your goals is to be able to draw things from your head? The books will not aid you with that. What it does do it help you start to put aside what you think things look like and what they actually do look like. But only to the extent where you might become an adequate copier. I don’t think it’s something to get too hooked on; there are other far more useful techniques for the long haul. Still it’s worth looking at along with other things.

I to recommend you just go and look through the conceptart.org forum, you don’t need to join in but it has a lot of helpful stuff on there. It’s really not just a place for professional concept artists, it went well beyond that a very long time ago. It’s a place of learning, for both beginners and god DAMN amazing artists. The finaly finish forum will bring such joy and feelings of inadequacy.

I'm personally not a naturally gifted artist in the slightest, but I've needed to learn some "tricks" for doing game sprites. So I don't really have any tips about drawing, but here are a few for doing sprite work. Not sure if any of these will be useful to you or not:

- Shading is important, and can be (and often is) as simple as lightening the edge of an object that's facing where light is coming from, and darkening the opposite edge. This will make something look like it has depth and three dimensionality to it. If you shade things in the OPPOSITE way, it will look like it's a depression rather than a bump. You'd be really surprised how big a difference this seemingly simple concept makes.

- Never underestimate the power of filters and "cheats." Download The Gimp and play around with its various filters. I personally find noise filters to be incredibly useful. They can add some subtle texture to what otherwise might look like a rather cartoony picture.

- Get help from someone else. MY brother and I are both working on a game currently, and he's been helping out a lot with the visual design. Just having someone else to point out when things don't look consistent or could look better is incredibly useful. Especially if they can identify exactly WHAT looks wrong.

-Blur filters. Sometimes, they can "gloss over" things that look bad :3.

- Start with something abstract. It's a lot easier to make pretty patters or even terrain than it is to make characters or 3 dimensional pictures.

- Experiment. It's really REALLY important to just TRY something. To dive right in and start learning by trial and error.

Get a piece of paper and a pencil. It's cheap. You would have to worry about too much stuff when starting out digitally on a computer. Draw as big as possible.

Use a reference for the helmet and make some studies. If you don't have a real helmet, you could draw metallic objects to observe the material. Draw a pot to learn perspective and to train your hand eye coordination (basically two ellipses connected by lines...draw the hidden lines of the ellipses as well).

Here's a great tutorial for some basic and advanced stuff: http://itchstudios.com/psg/art_tut.htm

If you want to go digital later on, buy a wacom tablet. Photoshop is nice, but there is also paint tool sai, corel painter, open canvas, artrage, alchemy...

Post your stuff on Newgrounds and get feedback. Or try DeviantArt.

Don't you think that attached image is not looking completely realistic? ;) That's why I said Illustrator is mostly for "animated" / comics pictures. I can not say you can draw in Illustrator, but with usage of plugin I linked + tablet you can get much more better effect in terms of realism. Just compare final effect of this movie with your attachment:
http://www.youtube.com/watch?v=8kzg_hF-CA0

If you have the money and some time, you could try taking an art class at your local community college. Otherwise, just keep drawing, really.