I believe that your ‘sound’ is in your fingers, so all that’s needed is an instrument that will facilitate your technique in the most positive way possible.
I find that I prefer a smaller bodied guitar and one that has medium size frets. The action needs to be very low, almost so there is none at all, and the guitar also has to have a tremolo system and impeccable tuning.
I don’t use many effects, I guess I’m more in the jazz camp than the rock on that front. In fact I only use one multi-effects processor and that’s the Yamaha DG Stomp.
It’s quite an old piece of kit – I think, 1990s. But it was developed with Allan Holdsworth (and Frank Gambale, I gather) so it has got that stamp of credibility, but never mind that, it’s the best modeller I’ve heard.
And, in keeping with the DG series,I’ve used the DG80-112 amp for years now. Best cleans ever.
I get my ‘synth-like’ guitar sound from the BOSS PS-6 Harmonist (blue pedal), set one 8ve up with a tiny amount of concert pitch and a massive amount of mids, it sounds very powerful – not like those horrible pitch-shift devices that try to imitate 12 strings. This has a wonderful sound that makes soloing much more fun.
For recording, I use an Alesis Q49 for all MIDI keys, and a 2018 iMac, running MOTU Digital Performer 9.