Sounds like you want DraftSight. DS offers a light version and a 30-day professional version trial for free.
I wouldn't say that 2D AutoCAD is an absolute necessity for learning SW. The 2D sketch feature is similar but SW is more geared to solid and surface modeling.
If your goal is to learn SolidWorks, Do not learn AutoCAD 2D. AutoCAD will teach you nothing but bad habits with respect to 3D parametric CAD. If you want similar software to AutoCAD, Draftsight is practically identical to AC Lite, and there are other free substitutes. if you want software similar to SolidWorks, the nearest thing in my experience is Inventor. Pro/E is the biggest competitor--but the interface is quite a bit more difficult to pick up. NX, SolidEdge and Catia also exist.
There are free 3D parametric CAD programs which you might poke around with, but these are not normally sought after by hiring corporations.
Honestly, I wouldn't recommend using any 2D software to try and learn SolidWorks as Mike Pogue has mentioned. Once you know one CAD software its very easy to hop to another as many functions are the same, just the buttons are different and the names might be slightly different. I went from Solidworks, to NX, to SolidEdge in about 5 years total time and it was all easy once I had a background in CAD.
....unless your talking API ...?