Which instrument(s) to learn?

There are two main instruments which you could use to play all of these, assuming you want to play a tune not just a beat in which case you might also want to consider a drum set. The first of the instruments is a piano or keyboard. Both of these will allow you to play a wide variety of music from Classical to Jazz to Organs and everything in between. Piano would also be good because it's what a lot of musicians use to tune their instruments since it takes a long time for a piano to lose it's tuning. The only problem with piano would be the immediate cost which is generally more than other instruments, its large size and the inability to create a sound. By which I mean a C note will always be one sound on a piano, where as with stringed instruments you can create sounds with pedals and bends etc.
The other instrument would be the guitar, which I know a little more about as I've played a slightly large selection. First off you seem to be interested in an electric guitar as these would better suite the genre you want to play. Next you would want to be getting a guitar from Gibson and Fender (those being the most common) guitars. Avoid ESP and Ibanez as these guitars give a much heavier sound which is more suited to Heavy Rock / Metal music. The pros with this would be that you would be able to take the guitar around with you, it's relatively easy to get the basics on the guitar and it can play a lot of genre. However the problems with a guitar would be that it's expensive in the long run, you need to change strings quite often depending on conditions which can cost a lot and changing them can put you off practice. Also every time you change the strings you need to make sure they're the same size and you have to retune nearly every time you want to play.

Hope that helps and if I can be of any more assistance please just let me know

woah woah woah, hold the fug up...are we talking keyboards, or actual pianos?

I'm talking about a Keyboard. Since he was saying his mum will pay for lessons I doubted he could afford a full piano. My referral to pedals was to do with the WAH-WAH pedal of a guitar. Whilst you can get effects for a keyboard they don't quite have the... human ability to be random as I was trying to show a negative.
Sorry if that wasn't clear.

oh ok that's fine then haha....I know what you mean with the guitars. Seems a better option for OP

Hey

Was listening to some blues a few hours ago and just a moment ago in the quiet of my house I have this tune in my head that I made up and am p1ssed that I can't play it on anything. It's not the first time so I'm going to learn to play it doesn't happen to me again.

What instruments do you think cover blues, classic rock and jazz best since that's kind of the area I like most. I'm thinking probably I should learn to play the piano and guitar but not sure.

Already bribed my mum to start paying for lessons as soon as I decide so just trying to think this through