DAW is a digital audio workstation. This is sometimes used to refer to the interface that sends audio data to the computer, and sometimes to the software that is used to process and store that data. OK- Understand that even if we had all the answers to the questions I am about to ask, there would still be a bewildering onslaught of different answers to your question.
Let's start at the beginning. You are recording into a digital recorder, but you want to record into a computer instead. For starters, why? Obviously you expect the computer to do something for you that the digital recorder can't do, so what is it? More questions- what digital recorder do you already own? What microphones? Any studio monitors? Headphones? Instruments, amps, etc.? You say you want to use a computer. What computer have you got? How much RAM, what kind of processor? How many hard drives, and how big are they? Do you have firewire? What kind of sound card?
Moving right along, what are you trying to do? Most importantly, what are you trying to record, what is the maximum number of tracks that you need to record simultaneously? Where do you expect this music to end up? Are you trying to make MP3's to listen to with your mother, produce a credible demo to promote your music, make a radio-ready CD? Planning on recording other people? For money or fun?
Next, what kind of space do you have to record in? Is there a lot of background noise? If you clap your hands. does it reverberate and come back to you? How high is the ceiling? Is it square? carpeted? windows? curtains? (pictures are worth 1000 words)
Lastly, what's your budget? What are you planning on spending right now, and what realistic investment are you prepared to make going forward?
I hope that you can see that different answers to these questions would produce very different advice, even if we all agreed, which I guarantee we won't. Nobody has all the money they want to do everything perfectly, so we all have to decide what is a priority.
In order to make a reasonable guess on the priorities, we need to know what you already have, what you are trying to do, where you intend to do it, and how much you can spend.
What we give back can only be as useful as what you give us. Make sense?-Richie