That’s a really open question as good tone is in the ears of the listener. What you like may be different from the person next to you and visa versa.
There are plenty of people on the forum with much better knowledge of how to nail a tone than me but for them to help, your first step should be to try to quantify the tone you’re looking for?

Do you want a single sound similar to a favourite musician, e.g. Clapton, SRV, Gilmour, Gary Moore etc etc? Or do you want to have a range of tones?

What don’t you like about the tones you’re currently getting. Too bright? Too dark? etc

Your biggest decision on a guitar is whether it has single coil pickups (e.g. Strat or Telecaster) or Humbuckers (e.g. Les Paul). Those will have the biggest impact on the sound it makes. Sure there will be a myriad of other details but that’s the key. Some guitars (PRS is a good example) have pickups that can be ‘split’ (my PRS SE Pauls does this) which allows you to have each pickup behave like a single coil or a humbucker to give you a range of sounds, though maybe not with the fidelity/nuance of a guitar that’s dedicated to one type.

I can’t really comment on your amp options as I’ve not tried either of those.

Most of us ‘chase tone’ in one way or another and will always be tweaking. All the additional elements you mention like strings, pedals etc will affect that, but sort the basics out first by identifying what you’re looking for and find the guitar and amp to suit that.

Intonation is really a one off thing, It shouldn’t change much if the guitar has been properly set up in the first place and a good store can check that before it’s delivered to you.

I’d recommend using your ears at your local guitar store with some guitar and amp combinations to help you home in on what you’re looking for. Or maybe you could arrange a trial of that PRS at home with your current amp options?

Andy has given you some excellent advice and info. I have an Ibanez RG550DX and think it sounds good but I prefer my PRS CE because it has a much wider range of tones. I think the pickups and the body wood make the difference. I also have a NuX MG 300 and it is pretty impressive. I think the Boss TU 3 is unnecessary (it’s not a strobe tuner by the way). If you ask most seasoned professionals they’ll tell you tone is in your fingers. I find that to be true but also think everything you mentioned also determines tone. Good luck on your quest for tone…that is a never ending search!

A few years ago I finally realized something: The gear that a person NEEDS depends entirely on how they plan to use it. If you plan on being an on-stage performer, you need stuff that will sound good on the stage. If you are a bedroom performer, you need stuff that sounds good in a small room. If you are a Youtube performer, everything can be post-processed, so you just need the gear to do that.

Mick said this: You can’t always get what you want. But if you try sometime, you just might find, you get what you need.

Assuming your guitar is setup correctly and in tune, the following have the largest effect on tone:

1. The pick you use – seriously, this will dramatically change sound and attack, especially on an electric. Your fingers also affect the tone if you don’t use a pick.
2. The amp – the amp sets a baseline tone. A fender amp does not sound like a Vox . Pedals can mimic the sound of a different amp, but not entirely.
3. The pickups – this is 80-90% the sound of an electric guitar, imho. The woods, hw, etc, have more to do with the feel and response.

Those are the 3 things I would focus on when seeking the tone I want. However, I also prioritize feel when it comes to a guitar. If it does not feel great I will not want to play it.

Just my observations so hope it is helpful.

Finding a guitar you are passionate about and want to pick up all the time is going to make you a better player. Whether that is design, looks, feel, can vary from player to player.
SRV played a Strat with single coil pickups through a loud Fender amp. So if you want that sound, there are a plethora of Stratocasters and Fender now makes a volume scalable Super Reverb. That will get you in The ballpark.
But if you just get a Strat style guitar and plug it into your DAW with an amp simulator you can get that sound d.
Strings…they are cheap and easy enough to try a variety till you find what you get what you like. I like D’addarios.

Robin Trower – Love Robin Trower!!! I saw him twice just before COVID hit and he really put on great shows.
Robin uses a 100 watt Marshall amp CRANKED!!! loud with a Fulltone OCD overdrive pedal and a pedal that Fulltone made for him that is like a Wah pedal that is partial engaged

With the NUX pedal, you should be able to approximate that tone but it will take some patience.
Suggest that you look for a forum or user group and see if you can find either patches or someone that might advise you

Correct me if I’m wrong – the Fender Excelsior tube amp has a 15″ speaker with a Volume control and Tremolo control but no tone controls. Very cool amp – Guitar Mic & Accordion inputs with a Bright/Dark switch.
With the NUX pedal, this amp should get the job done for you – but patience in setting it up. Like I said, this is a very cool little amp with tons of tone and capabilities

This is amp that you set the volume at a certain level on the amp and use the volume and tone controls on your guitar. I’ll include some videos below

Try each input to see which sounds best because the impedance of each input will vary the tone slightly

I’m a believer in the law of diminishing returns. As we spend more and more money on gear, we see less and less of a difference between the rungs of the ladder. Going from a $100 guitar to a $500 guitar- you’re probably gonna notice a big improvement. Going from $2100 to $2500? Not so much. Applies to all things, including strings and amps.

It’s not just about the money you’re spending, of course, personal preference comes into play. Money doesn’t always tell you how good a piece of gear is- I guess my point here is you could certainly see a difference with something new, but I don’t think you need to put yourself into the poor house to do it.

It does really sound like that Ibanez is limiting you, possibly the set up, the tone- or both. It also sounds like that PRS suits you better. You say it feels “precise” which is a pretty good sign in my book. It does indeed sounds pretty inspiring. Can you get it on a trial period?

The other pieces (Nux, fender amp) seem pretty solid, my guess here is the guitar is the weak link. I will however give a shout out to Positive Grid Spark. I love mine . It has the modeling and FX, like the Nux 400- but also the speakers are pretty great and may give you more play options. Just all depends on your day-to-day practice routine.

As for intonation, this is a normal part of guitar set up. Yes, you should learn to do it yourself- eventually. It’s also a great idea to have a tech do it your first time, and get it dialed in to your preferences. Then you’re just making micro adjustments as the seasons change. Bonus points if they let you watch!

Best of luck!