Hello JJ and welcome.
You need to consider how you want to proceed so that you get the correct advice for your particular case.
First thing, can you play an instrument and if so what? You say "expressed though computer processed music" and that would tend to mean a keyboard of some sort.
The computer is in many ways the least of your worries. Anything that can run Win 7 or later will surely have the power to run a couple of dozen tracks and a few effects.
You will almost certainly need an Audio Interface. This takes the analogue signals from microphones, guitars, keyboard if it has analogue outputs, converts those signals to digital data and sends that, almost always by USB, to the computer. Then, MOST importantly it converts the computer output back to analogue for you to hear. You might know that all computers can do this? So they can but badly, very badly as a rule.
With the AI will come recording software, usually called a "DAW". This could be Cubase or Ableton or any of several others. All have their strengths and weaknesses and some do certain things better than others. All the major DAWs can be downloaded and tried for a limited period. Many, many people rate Reaper and it certainly is very good and very cheap.
What is your budget?
Dave.
Dear Dave,
I have pm'ed you. Although, I am unsure whether it went through or not....hmmm...
Have a great weekend!
JJ