i know i'm picking this up a bit late and it looks like you're very happy with the response you got from dillodude
but i just thought i'd offer some alternatives out there...
i use ableton live which is a professional daw (digital audio workstation) aimed mainly at djs and producers and live use. it is a great daw though, very user friendly and powerful with great tools, synths and sounds included. it is quite expensive though, obviously depending on whether you just wanted something that could help you compose music for your games or whether you wanted to start to build a bedroom music studio! well ableton live intro cost around £100 i think so...
however, if you're looking to get a midi keyboard controller to help you compose, you'll find that many are bundled with cut down versions of professional daws to help you get started. many keyboard brands come with ableton live lite, or other daw software. here're some examples of smaller, cheaper keyboard controllers that come with software, that you might consider...
alesis q25
korg microkey
m audio axiom 25: i've got this, bit more expensive than the others but does have mpc style drum finger pads and some knobs
anyway other than all that there are lots of fairly good and free daws that are available out there. some that i'd recommend:
musagi: a mini daw, very easy to use, designed for old skool videogame music (8 bit/chiptune) in mind. but can do lots more. definitely worth checking out, especially if you're looking recreate a mario style theme tune!
http://www.drpetter.se/project_musagi.htmlmu lab: mini daw, simple to use, can be upgraded as well
energyxt: not quite free but cheap
these are all sequencer based daws which are probably the easier to understand than the old school tracker types, most of which are free. one to check out though would be renoise. this is great, cheap not free, i've been mucking around with it but much prefer working with a sequencer, i dunno what's going on half the time with a tracker!
if you're not sure or you want to do some research go to
http://www.kvraudio.com/ this has lots of info on computer music and production. main advice would be try out the demos of some small easy to use daws and see how you get on
hope that's some help