Inna, that's the way it goes into the computer interface, and then into the computer. We went round and round, right here on the PC forum about which "interface" and they were discussing which "audiophile" card to use on Stereophile. In order to cut corners I modified an interface so heavily, I had to build a different case.
But that's the way to go, straight from the Phono output. It's for sure you got the right idea. Although the computer stuff didn't cost much (as audiophile equipment goes) there was a lot of need to know for that project, and I don't know where you can find it all.
The final outcome is just as good as the way you're talking, and it's so much more convenient, because you have a library for your reel.
Have fun.