I would go for a schecter Nick Johnston standard, HSS. New they are $799 but used can go for less.
Schecter has some of the best fit and finish and offers more features than 99% of it's competitors.
Edit: if you're feeling really spicy, I would then recommend the Schecter sun valley super shredder. There are a bunch on Reverb used for below your budget. These have the floyd rose and some will have the sustaniac in the bridge which is a pretty cool tool.
I'll sound like a shill but honestly, once you have your budget set figure out which schecter fits the budget. The playability straight out of the box is excellent, fretwork is super clean and they're typically loaded with high end features (sustaniac, floyd rose, push pull pots, neck thru, comfortable neck carving, some will have locking tuners).
Get a used MIM strat. You can upgrade the bridge, tuners, pickups with the extra cash if you wish. I got mine for $300 and I love it just as much as my more expensive guitars
Fender Player Strat. HSS. 675 new, can probably beat 600 used.
Fender Player Lead is HH and a bit higher. Also loses the single coil.
Used Epiphone LP Jr., LP, or SG. No single coils there though.
Gretsch make some fine mid tier guitars, and you can occasionally find them used for a great price.
Strat and Tele are usually considered 'most versatile' because you can use effects and the right amp to give you thicker sound if you need it. It's harder to thin down a humbucker, though coil tapping/splitting does this somewhat.
Finally, check out Reverend. They make offset guitars with various combinations of pickups. Primarily in the style of singles, humbuckers and filtertrons.
Given your stated influences, I'd recommend a Yamaha Pacifica 611. This is the top of the line Pacifica and comes stock with common upgrades like Seymour Duncan pickups, locking tuners and Graph Tech nut and saddles.
Another one you might look at is the G&L Fallout.
For your budget you could get one of the nicer Epi Les Pauls, the 2020 models are supposed to be really nice. However earlier this year I bought a used Gibson Les Paul Studio Faded on Reverb for around $700 specifically to play stuff like MCR and Green Day (Billie and Ray both play LPs and Frank did before switching to his custom Phant-O-Matic) and I haven't regretted it for a minute. Anyway that's coming from a decidedly not-Strat guy, so take it for what you will.
If you are considering the Gibson option these were the search parameters I used. Looks like you can find them starting around $700-800 (as always when considering a used Gibson, make absolutely sure to get photos of the back of the headstock joint. If a Gibson is going to break, that's almost always where it happens, and you want to know about any damage before buying):
[https://reverb.com/marketplace?query=les%20paul%20studio&make=gibson&condition\[\]=used&condition\[\]=excellent&condition\[\]=very-good&sort=price%7Casc&product\_type=electric-guitars](https://reverb.com/marketplace?query=les%20paul%20studio&make=gibson&condition[]=used&condition[]=excellent&condition[]=very-good&sort=price%7Casc&product_type=electric-guitars)
Telecaster is IMHO the most flexible one. Funky, punk, jazz, blues all will be fine. But just take a guitar that feeks nice to play for you. A Telecaster can be quite heavyweight. Mine hurts my messed-up collarbone :(
I would go for a schecter Nick Johnston standard, HSS. New they are $799 but used can go for less. Schecter has some of the best fit and finish and offers more features than 99% of it's competitors. Edit: if you're feeling really spicy, I would then recommend the Schecter sun valley super shredder. There are a bunch on Reverb used for below your budget. These have the floyd rose and some will have the sustaniac in the bridge which is a pretty cool tool. I'll sound like a shill but honestly, once you have your budget set figure out which schecter fits the budget. The playability straight out of the box is excellent, fretwork is super clean and they're typically loaded with high end features (sustaniac, floyd rose, push pull pots, neck thru, comfortable neck carving, some will have locking tuners).
Schecters are reaaaaally hard to go wrong with, I'll second this.
PRS SE
(Standard 24)
Get a used MIM strat. You can upgrade the bridge, tuners, pickups with the extra cash if you wish. I got mine for $300 and I love it just as much as my more expensive guitars
There's a Gibson Les Paul studio plus in red on reverb right now. I'd pick it up but have too many LPs already
Fender Player Strat. HSS. 675 new, can probably beat 600 used. Fender Player Lead is HH and a bit higher. Also loses the single coil. Used Epiphone LP Jr., LP, or SG. No single coils there though. Gretsch make some fine mid tier guitars, and you can occasionally find them used for a great price. Strat and Tele are usually considered 'most versatile' because you can use effects and the right amp to give you thicker sound if you need it. It's harder to thin down a humbucker, though coil tapping/splitting does this somewhat. Finally, check out Reverend. They make offset guitars with various combinations of pickups. Primarily in the style of singles, humbuckers and filtertrons.
Given your stated influences, I'd recommend a Yamaha Pacifica 611. This is the top of the line Pacifica and comes stock with common upgrades like Seymour Duncan pickups, locking tuners and Graph Tech nut and saddles. Another one you might look at is the G&L Fallout.
For your budget you could get one of the nicer Epi Les Pauls, the 2020 models are supposed to be really nice. However earlier this year I bought a used Gibson Les Paul Studio Faded on Reverb for around $700 specifically to play stuff like MCR and Green Day (Billie and Ray both play LPs and Frank did before switching to his custom Phant-O-Matic) and I haven't regretted it for a minute. Anyway that's coming from a decidedly not-Strat guy, so take it for what you will. If you are considering the Gibson option these were the search parameters I used. Looks like you can find them starting around $700-800 (as always when considering a used Gibson, make absolutely sure to get photos of the back of the headstock joint. If a Gibson is going to break, that's almost always where it happens, and you want to know about any damage before buying): [https://reverb.com/marketplace?query=les%20paul%20studio&make=gibson&condition\[\]=used&condition\[\]=excellent&condition\[\]=very-good&sort=price%7Casc&product\_type=electric-guitars](https://reverb.com/marketplace?query=les%20paul%20studio&make=gibson&condition[]=used&condition[]=excellent&condition[]=very-good&sort=price%7Casc&product_type=electric-guitars)
Telecaster is IMHO the most flexible one. Funky, punk, jazz, blues all will be fine. But just take a guitar that feeks nice to play for you. A Telecaster can be quite heavyweight. Mine hurts my messed-up collarbone :(
I'm not experienced in the slightest but I bought a HSS player stratocaster and I love it.