First of all, do not think that the sound you hear has a lot to do with certain strings or amps, pickups or whatever. It's just how I play. So, don't expect that some special gear will give you the ideal tone, you mainly need good technique, to get good tone. Having said that, below is what I use most.
Guitars: Peerless, Elferink, Epiphone.Videos done in my home studio involve no amp at all, I just plug into my PC (I'm currently using a lexicon USB audio interface), running Cubase, adding a very mild reverb (plugin) to remove the dryness and a very mild compression with slow attack. The amp I use for gigs is usually a Sessionette 75; it has a good clean sound, although a bit sharp, so I cut back the treble a bit. As for strings, for hollowbody guitars I use .012 or .013 flatwounds, but also regular, various brands. For semi-hollow I use regular strings, .011 sometimes also .012. The picks I use are a medium heavy, not too heavy but definitely not too light.
I've never been into looking for the ideal strings, the perfect amp, etc, so don't ask me advice on that. Anyway, perfect does not exist, plus it's very personal. Get something decent and work with it!
For me it is important that a guitar has a good feel, good intonation, and feels comfortable to play. Of course it has to have a decent sound, but, the main part of 'the sound' is how you play it. So, if your question is if I changed anything on my guitars, the answer is no. If I don't like it, I sell it, and buy something else. I'm just not into modifying guitars.
Finally it's just a matter of practice, to develop good tone. I guess my classical training helped a lot. See also the Technique page.
On some youtube videos you will see a black Roland GK-2 midi pickup attached. I use it only to make midi/TABS/notation out of some solos I play, so it has nothing to do with the sound.The midi is also used for the fretboard visualizer in my jazz exercises package and the fretboard videos.
For practising, I can recommend using a loop pedal. I recently got a Digitech Jamman. It's great to play some backing chords and then jam over them, it's an entertaining way to practise.
Below you can see 5 videos where I play guitars from luthier Frans Elferink in his studio.
The Club amplifier from ZT Amplifiers: small but powerful. I like the size and looks already, but the sound does not disappoint either. Plenty of punch, but smooth enough to play jazz, overall pretty good in fact. You can dial in a bit of drive if you want, and it has a decent reverb. Effect loop and some other external connections make it complete. It's simple but good, that's how I like it: you plug it in, and it sounds good, no tweaking and fiddling needed. Just Plug-and-Play!
You can find a video of me playing it on the ZT Amplifiers YouTube channel.