Yeah, there are tons of great options. Reaper is great because it is inexpensive, but it does really lack some heavy duty features that you may want later, but it is simple in form.
If you are really looking to compose and do sound design and not really record, take a good look at Reason. It has all of your traditional sounds, plus some crazy synthetic sounds plus all the sound design tools you could need. The downside is that it doesn't do recording in the traditional sense. They are releasing Record to be the companion piece for it that would cover that aspect if that is what you feel you need.
If you would like to talk about it more, I would be happy to help you. I own and use all of the major DAW software.
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