I would start with the built-in tutorials (under help->SolidWorks Tutorials) that should at least get you familiar with the features and terminology.
I'm sure you'll find a wealth of knowledge and many very helpful people here.
Don't be afraid to ask questions, no matter how simple they seem. I was with Mech Desktop for 10 years before switching to Solidworks 12 years ago and I still learn new things just by watching the forums for interesting topics. (Plus it's comforting to know that other people rant about the same issues.)
Glad to have in the discussion group. I would highly suggest finding the closest SWorks User Group to your location also. There are a large number of them throughout the World. You can find the listings on the Community section of the SWorks Customer Portal. No charge, no commitment, just good people sharing and learning like you!
You can learn the most the fastest with the tutorials for a while.
Welcome to the group.
I'm in the same boat as you, with over 20 years of NX, which I found to be pretty straight forward, all the functions off of the MB3, etc. and having been bashing my head against the keyboard in attempts to work with SW. As you mentioned modeling process aren't that hard and the concepts are similar- much more limiting in SW-but that’s from my point of view. When it comes to learning this system the hard part is mapping commands and functions that have become more of habit to the new system.
When it comes to drafting I find it interesting that SW appears to have adopted an AutoCAD approach with controlling titleblocks, titleblock text and then the drawing views..my opinion these "layers" to the drawing make things harder than they should be.
It's this level of change that affects the "habits" we've been used to that are difficult to overcome. Keep it up and remember you are habit breaking and forming...it will take awhile..and can be painful as I can attest to the waffle printing on my forehead from the keyboard!
As for training, a good, inexpensive, online source is the igetit subscription training. I find it interesting that the OEMs haven't figured out that they truly need to offer "Transition" courses. igetit has one but its AutoCAD to SolidWorks. Siemens offered a free Pro/E to NX and an I-deas to NX course at one time in their Learning Advantage subscription.
My pet peeve: DON'T repeat the use of the same icon for "similar" functions!!!