There's not really any 'good' software. If you're untalented, no amount of money you throw at sequencers and DAW's is going to make you any better.
Here's my take based on my experience working with some different DAWs:
- Garageband: if you own a Mac, it should have come pre-loaded with Garageband. It's not the greatest software in the world but in the hands of a talented composer, it can be just as good as professional-grade DAW's.
- Logic Pro: fully integrated midi support, tons of pre-sets and synths that you can mess around with to create custom sounds, and it comes with a lot of effects and plug-ins. It's also really easy to use any virtual instruments or software plug-ins (compressors, amp sims, effects pedals, etc.). It looks and works a lot like Garageband, so if you start with GB and move up, Logic will feel natural, if more advanced.
- Pro Tools: designed more for studio recording than actual composing, although as of Pro Tools 6 (I think) there is midi support. You can still write/record midi and use your midi keyboard: if you're going to be doing more recording than midi-ing, Pro Tools is definitely the way to go. It has a crap-load of built-in effects. At first, it's a little less intuitive than Logic Pro, but you can also do a lot more in terms of plug-ins, side-chaining, and generally messing around with audio files.
- Digital Performer 7: this is not software designed for your typical amateur musician. DP7 is, as they say, srs bsns. It is literally everything you could ever want: a full sequencer/DAW, full audio import/recording support, SMPTE time code functionality (very helpful for film composition) and it has complete built-in mixing and mastering suites. Not to mention the amp simulations and modeled effects pedals which are just completely sexy.
- Magix Music Maker: it's a bit like Garageband, but they both do different things. Music Maker seems geared toward more electronic music production, whereas Garageband is more accommodating to different genres. If you stay away from the pre-set loops, Music Maker actually has quite a bit of functionality to offer: a generous amount of editable synthesizers, drum sequencers, a nice amount of pre-set audio effects, "Elastic Audio" (a.k.a. Auto-Tune), as well as built-in mixing and mastering functionality that is a bit more advanced than Garageband.
- Audacity: open source + free = good, in my opinion. It's not got a whole lot of functionality outside of audio recording. I generally use it for rough mixes (sometimes final mixing) and for exporting my work to high quality mp3 (320kbs variable), and reading/writing 'non-common' or OS-dependent formats (like FLAC, OGG, AIF, etc.)
That's just barely scratching the surface, though. There's a ton more software available out there and, as I said, having the most expensive DAW doesn't compensate for natural talent. And just because you use a free or cheap DAW doesn't mean you can't still write good music.