What are some alternatives?
When comparing Logic Pro and Reaper, you can also consider the following products
LMMS - Make music with a free, cross-platform tool
FL Studio - Image-Line's FL Studio, now on it's 12th version, is a well-known music production suite and the most popular beat processor on the market, due no doubt to its longevity. Read more about FL Studio.
Audacity - Audacity is a free and open-source audio production software suite that includes a surprising array of editing tools and recording systems.
Ardour - Record, edit, and mix on Linux, Mac OS X, and Windows.
GarageBand - GarageBand is a fully equipped music creation studio for Mac
Ableton Live - Ableton makes Push and Live, hardware and software for music production, creation and performance. Ableton´s products are made to inspire creative music-making.