Morphio,
If you want to look into bars that aren't so deep, consider the Nitto B125. They are "short and shallow". They have similar reach and drop as the popular 3T Scatto, but at a fraction of the price. You can probably find these at a local shop that caters to the track or fixie scene.
Aluminum or steel will suit you just fine.
They only come in 25.4 bar clamp sizes. So, you'll either need to use shims (which will hold just fine) or find a 25.4 stem.
They should start at around 50 pounds sterling for steel and go up to 70 for aluminum alloy (both are very strong) and the aluminum variant is very light.
Narrow road bars will due, as well. Assuming that you won't participate in events that require a standing (or near standing) start like kilo, keirin, match sprinting, etc... Road bars have a very wide "top" which impedes the forearms during standing starts and will kind of make it awkward to do them. This is why track bars immediately slope downward as the bar moves away from the stem. If you are doing a normal new racer's race program, you'll likely do a bit of everything.
If you plan on doing strictly mass start racing (points, scratch, madison, etc...) then road bars will be fine (just pick a narrow set 40cm or less). Road pars are preferred for Madison for the hand-hold area up top during exchanges.