The good turntable and DJ mixer is fine. You’re already head and shoulders beyond most people trying to do this.
If you have a “real” sound card with all three (or more) connections (pink, blue, and green) then you can get the appropriate sound adapter…
http://www.radioshack.com/product/index.jsp?productId=3452165&CAWELAID=343437415
…or equivalent for a lot less money. Pick the blue (usually) connection on the sound card which is normally high-level stereo Line-In.
Configure your computer and Audacity and go to town. I make that sound so easy
You may find that the sound in your built-in card is noisy which is normal. The electrical radiation environment inside a computer is aggressively hostile. (“What’s that warbling buzz in the background?”) This is when you pop for an external USB sound card with Line-In connections.
https://forum.audacityteam.org/t/sound-card-reviews/8375/1
Macs come with a terrific Stereo Line-In and it isn’t noisy.
Koz