Just remember that composing is a skill that requires formal training; != mastery of software. Software and hardware are tools for you to apply your composition skills, and are no substitute for solid musicianship, theory, and writing skills.
My recommendation for a first-timer would be to seek instruction at a community college or other educational resource, where you can receive face-to-face instruction, under the tutelage of a trained musician and/or professional composer to learn fundamentals of music-theory, musicianship, and composition/songwriting.
Of course, in the popular vein of “songwriting,” one doesn’t necessarily need formal training to write and arrange songs, but to address your question of composing music, I believe there is a distinction.
As for software and hardware tools, admittedly I am mac-centric, and will echo the above recommendations.
@Eambos: Logic Pro Studio retails for $499. Apple will honor a $50 discount to faculty, staff and students of K-12 and higher ed. institutions (with proof of enrollment).
As for hardware recommendations, setting up your own project studio / Digital Audio Workstation (DAW) requires thorough research and $$. You should be aware that a professional-strength DAW that is outfitted for composing has the following components:
Computer (Fast, lots of RAM, large display(s), plenty of fast storage (7200rpm or faster hard drives);
Accessories and peripherals for the Computer and DAW: Power Conditioning (line conditioner to suppress EMI/RFI interference and voltage spikes), UPS backup battery capable of supplying power to all components tied to the computer in case of power loss; external hard drives for removable, fast storage (at least FW800 bus recommended);
Electronic Music/MIDI: Some sort of MIDI controller (preferably with an integrated USB interface), foot pedal, Digital Audio Interface (to get analog sound in/out of the system, e.g. when recording with mics, and when monitoring on external loudspeakers);
Audio input and monitoring: Microphone$ (can be costly), Powered monitor loudspeakers (or power amp plus passive monitor loudspeakers), cabling, speaker stands/mounts, studio-quality headphones; if you plan on recording with more mics than there are inputs on the audio interface, then you’ll also need an multi-channel analog mixer;
Accessories: Room treatment (acoustic paneling), Mic Stand, Mic Cable, Pop filter, headphone amplifier (if more than one person needs to monitor on headphones), furniture, Blank removable media (CD-R, DVD-R, etc.), printer, paper, etc.
Software: Make sure that whatever software you use, you have a computer system that matches the minimum system requirements for that program; in addition, there are third-party plug-in software apps that are designed to enhance sound and instrument options to your DAW; many of the DAW apps (Logic Studio for example) include virtual instrument and mixing plug-ins, but some don’t. If on Mac OS X, make sure the 3rd party plug-ins are AU, VST, or RTAS compliant.
Lastly, there are great textbooks available that discuss this very subject; might I recommend taking a look at a publisher I use for my audio curriculum, Focal Press (Elsevier); also you can look up the Apple Pro Training Series for Logic from Peachpit Press; they will provide you with ample background information that will inform your purchase and research.