It depends on just what you will be doing mostly. A laptop would certainly be quite useful if you were going to be doing on the road type of recording, but a desktop would be better for studio work.
As for the software that also depends on just what you need to do. You might be able to get by quite cheaply with something like Amadeus Pro which is a very good full featured audio editor program that allows you to record, edit, save, etc. Or you might need one of the professional type of programs.
What you will need, no matter which you use is a good quality mic to do the recording. Don't skimp on the mic other wise you will not get good sound quality. Something like a Heil PR40 or better would be well worth the price in sound quality.
Always save your recording in .wav format. If you want to reduce the size of the files to say an .mp3 format save it at the least in 192 or better yet 320 in order to have really good sounding files. These of course will be rather large, so that is where a good desktop will come in real handy with 2 or 3 large hard drives to work with.