Disclaimer: my opinion may be of limited value, since I'm relatively noobish, never compared DAW's and pretty much use one. Checked Ableton live lite once but was kinda underwhelmed due to lite version limits (only 8 tracks and couple of virtual instruments I think, at least in my copy bundled to an E-mu keyboard).
Anyway, I'll write couple of words about
REAPER from a perspective of person who pretty much started playing around with sounds thanks to it. It taught me a lot about digital recording stuff, before REAPER I was pretty much all huurr durr derp about audio recording and editing. Now I know bunch of stuff about multitrack recording, editing, parameter automation, using virtual instruments, routings (REAPER has it perfected apparently), how to subtract noise from recordings (with bundled plugin), how sidechaining and drum replacing works etc. All with background reading reduced to minimum. It's nowhere near "industry standards" like ProTools in prestige but it's relatively young application (development started about 5 years ago) and rapidly gaining popularity - they also have excellent, helpful community at their forums and react for feature requests very fast.
It's very sleek, stable and optimized - installer for windows version weights about 5 megs, OSX version is couple of megabytes larger, has 64 bit versions too. There's plenty of plugins included - mainly effect/production ones, only rudimentary synthesizer for testing purposes - so you need to gather a rack of virtual instruments and samples by yourself. Accepts VST/VSTi/DX (win)/AU (OSX) plugins and rewire connections. As I said, it's very stable, only thing that can bring it down are shoddily coded plugins, but it should be pretty safe too, since from version 3-something it supports spawning plugins to separate processes so dying plugin won't fuck your whole session up.
Shortcomings I know about - some people mention MIDI editing abilities a bit less sophisticated than in let's say Cubase products - but you have to do pretty advanced things to notice it I guess. For me, handy MIDI editor in track, editing, humanize/quantize and swing settings are enough. Other than that - I don't know. Every time I think REAPER lacks something brief visit on the forum reveals that REAPER does it too.
Oh, and I like their bussiness model. Demo version differs from the registered product only with 5 second nag screen upon startup - otherwise it's 100% functional. Absolute lack of pain in the ass DRM :>. I paid for the licence not because they were forcing me to but because they're super nice towards the potential customer.
So, in short: yep, it's fit for recording, editing, adding drums and other musical shit

. Hope that above was somewhat helpful.