These are the programs I use. None of them are free.
Finale – Notation
Logic – DAW
Max MSP – I don’t know what you would call it. It synchronizes multimedia.
Some free alternatives:
Finale Notepad – The lite version of the notation software I use. Should be able to export MIDI.
TuxGuitar – Notation, can import and export MIDI and Music XML. I try to avoid it, but it can get the job done.
LilyPond – Notation, requires more skill to operate.
Anvil Studio – MIDI sequencer, seems to be more along the lines of what you’re looking for. I haven’t tried it.
Reaper – DAW
Ardour – Another DAW, more flexible, but requires some know-how.
You can probably find some free sample libraries and a sample host somewhere on the net.
or try FL Studio and export your projects as a midi file ^_^
Recommended budget controllers:
M-Audio Keystation series (already mentioned)
M-Audio Oxygen series
Roland Edirol PC-50 (or 80 or whatever)
Alesis Q-49 (or 61, etc.)
Korg K series
^ Note that "MIDI controller" means that they don’t come with sounds – they only trigger MIDI. Sounds come from a synthesizer or from a sample library.