Now lets get to the subjective side of how music sounds at these different bit depths and sample rates. No one can really quantify how much better a song is going to sound recorded at 24/96. Just because a 24/96 file has 250 times the audio resolution does not mean it will sound 250 times better; it won't even sound twice the quality. In truth, your non-musically inclined friends may not even notice the difference. You probably will, but don't expect anything dramatic. Can you hear the difference between an MP3 and a wave file? If so, you will probably hear the difference between 24 bit and 16 bit audio. It gets real subjective hear as our ears are different. But lets try to be a little objective here.
Lets talk about sample rate and the Nyquist Theory. This theory is that the actual upper threshold of a piece of digital audio will top out at half the sample rate. So if you are recording at 44.1, the highest frequencies generated will be around 22kHz. That is 2khz higher than the typical human with excellent hearing can hear. Now we get into the real voodoo. Audiophiles have claimed since the beginning of digital audio that vinyl records on an analog system sound better than digital audio. Indeed, you can find evidence that analog recording and playback equipment can be measured up to 50khz, over twice our threshold of hearing. Here's the great mystery. The theory is that audio energy, even though we don't hear it, exists as has an effect on the lower frequencies we do hear. Back to the Nyquist theory, a 96khz sample rate will translate into potential audio output at 48khz, not too far from the finest analog sound reproduction. This leads one to surmise that the same principle is at work. The audio is improved in a threshold we cannot perceive and it makes what we can hear "better". Like I said, it's voodoo.
So should you record at a high sample rate? Its going to depend on who you ask. Some people say "It's all going to end up as 44.1 any way" when the cd is burned. Others will tell you that when an audio interface processes and mixes sounds at 96 kHz the result is better and remains better even after the final conversion to 44.1. And just about every other position is taken too. Some say 16/44.1 is good enough for CD its good enough for me. Others say do 24/44.1 because it's not that much more space and it increases the signal to noise ratio. There is one argument that says 24/88.2 is superior to 24/96 because it is an even number conversion going back to 44.1.
So what's that? You want to hear what _I_ think. Ok, this is the gospel according to Tweak! Use 24 bit for every recording if you have this feature. I was a believer for the past decade that 16 bit was the way to go and I have absolutely changed my mind. No matter of what you are recording this is true. If you have a nice mic, a very good preamp and a clean audio system and are recording highly dynamic instruments such as acoustic guitars, classical orchestras, acapella vocals, the difference will be there. Quiet passages will be less likely struggling to stay above the noise floor on your system. One can record with no compression. You can record at lower levels, with more headroom. This ensures that the occasional peak is not truncated at the top and it will give converters some room the breathe. Because you are not pushing the limits of your bandwidth, your instruments will sound clearer, and the vocals may sound "cleaner", the song will mix better and there will be less noise.
Regarding the sample rate, unless you have a good reason not to, use a sample rate of 44.1. If you are doing audio for video you might want to use 48khZ as many editors only use that rate. Some kinds of music seem to benefit slightly from the high resolution of 88.2 or 96Khz. Acoustic instruments, like guitars, percussion, and of course vocals, i.e., things with delicate high frequencies seem to benefit but its subtle. Lets say you had a $399 audio interface with onboard preamps. Replacing your preamp and converters with better ones will give you more of a sonic difference at 44.1 that recording at 96khz will.
Once inside the sequencer, audio files may be converted to 32 bit for processing and converted back to 24 or 16 on the way out. So, my advice is to record at 24 bits/44.1 at minimum and go up to a sample rate of 88.2 or 96 if you think your material warrants it (and you have the disk space.)