So, I have an Ibanez Gio GRX20, and a Line 6 Spider III amp.
I’m currently trying Jamorama.com’s free trial lesson, and enjoying it, and I also am plodding through Fretboard Logic.
Any hints and tips on how to learn effectively?
(Practice, practice, practice, I know…) 
Really depends on your genre and what the genre emphasizes. If you’re a jazz guy like me, I’d suggest you buy a chord book (Chord Master is great) and start memorizing chords. Learn scales, but don’t think of them as “positions”. Just learn the notes, because it is better to think in terms of notes than in terms of frets. And lastly, learn to read music.
And stay away from the Joe Satriani books for now.
At some point in the next 6 months or so take at least one lesson with an instructor who can see your technique and (likely) correct it. You are probably developing all sorts of bad habits right now and not even knowing that you are doing so. Simple things like proper wrist position are hard to learn from a book or website, even one with lots of pictures. These habits can be overcome, but will make progressing from beginner to intermediate more difficult at best, and cause long term physical damage at worst. So get at least a lesson or two in with someone who knows what they are doing.
If at all possible, as NAF1138 says, find an instructor, and take a years worth of weekly lessons (assuming you get on well with the instructor; shop around if need be, and find someone who teaches what you want to learn). When I started, I found just having someone to sit down with who knew a whole lot more than I did about playing made a huge difference. It’s also motivational – on a weekly schedule, there’s some pressure to work on stuff so you can show your teacher and get more stuff to learn. Success then breeds success.
I think learning music notation is probably a task well-deferred during your initial 12 months. Tablature is useful enough for now, when needed.