I'm a professional guitarist (with a jazz background), and I also play piano. What I'm reading into your question isn't a problem of "what should I learn", but "how can I apply what I already know?"
The two instruments are very different in their approaches. On the piano you've got one key for each pitch, but on the guitar you can get the same pitch on different strings. As a result, the application of the theory you know is straightforward on the piano, but on the guitar you need to visualize things differently.
Guitarists (in general) think in terms of 'shapes' - if you learn a chord voicing or a scale fingering, you can immediately play it in all 12 keys by moving it up or down the fretboard. If there are no open strings, a dominant 7th chord fingering will always produce a dominant 7th chord sound.
On the piano you can look at a chord and know which note is the third. On the guitar you have to think about which string is carrying the third in a voicing. Move it down a fret and you get a m7 chord - move it up and you get a sus7.
So in terms of getting a grip on chord voicings, learn the common inversions. For example, an F7 chord can be voiced 1x121x, 5x354x, 8x786x, or 11-x-10-10-10-x. (There are lots of other possible ways to voice it, but that gives you the root position and one of each inversion.)
Then for each of your basic voicings learn which note is on each string. 1x121x is R-b7-3-5 under your fingers. Grasp that for each voicing and forming a 7+ chord is o big deal - it's 1x122x. The m7 is 1x111x, and so on. But when you move to the next inversion, 5x354x is 3-R-5-b7. Making that aug7 chord means raising the 3rd string instead of the 2nd; each voicing is different, but the same principles apply to all of them.
For the noodling around part, learn the pentatonic fingerings first. Because of the way guitars are tuned, you'll have two notes on each string in any position, so there are only five fingerings. You can then add two notes to those patterns to form the major scale... but in most positions you're going to be stretching for one or more of the additional notes, which gives you more fingering options.
Being able to read standard notation on the guitar will really help with applying the theory you already know. For my students who already play another instrument I typically use the Berklee books - book 1 takes you through the basics of the "low neck", book 2 takes one key at a time through all the positions, and book 3 focuses on one position at a time in different keys. But since the guitar has more fingering options for any given note than the piano, be prepared for a longer learning curve.