What's your local building department going to require of your permit drawings? BTW, where are you located?
Do they need to signed and sealed by a local architect or engineer? What drawings are they going to require? I'd think a site plan, floor plan, roof framing plan, foundation plan, elevation of each exterior wall, and probably a typical wall section at a minimum. While most of those drawings are easy to generate with CAD, the wall section takes some practice. Don't know what your drafting / construction knowledge is but they can be difficult until you've done it a few times. Electrical drawing / service riser diagram may be a requirement too depending on the location.
As far as free software goes, you usually get what you pay for. The big exception to this Sketchup. Unless you spring for the pro version though, it will have limitations and may not be the best choice for developing all of the drawings you'll need for a permit.
Besides showing all of the pertinent information for the permit, you want to make sure that your drawing(s) have all of the information that you'll need to actually build the garage or have it built by contractors.
Let me know if you've got other questions. I used to do CAD for an architecture firm for about 5 years.