robvdp Greeting and welcome!
I'll be representing the Fender clan (kinda, I'm a strat fan)
I did write a little article to partially update Singe's wise words, Part I here
robvdp I would like an electric with an amp that can take headphones if needed (not sure if this is blasphemy lol)
Not at all....! It's always more fun to hear the roar of a guit in clear air - but headphones are useful if your neighbours are boring and if you enjoy stereo processing (ping-pong delays ftw), a bit cheaper than two amps
robvdp I am not sure how the quality of Epiphones are currently
Actually really good - at times better than a gibson (some even come std with gibson usa pickups). THough not all are equal, try a few to find one that speaks to you. One thing, is that your budget probably won't stretch to a new Epi LP + amp, etc...But that's okay, a good secondhand one should be around 3.5k-6k.
Alternatives to a Epi would be a Tokai. It'll likely be a a MIC one, but Tokai have good Q/C and there's a local distributor (Lance WIener) so there's good after sales support.
There's also a bunch of LP copies (Morris, Samick, Cort, ESP, PRS). For the metal addict, a ESP, for a rock n blues a PRS for vintage vibes a Morris and under no circumstance (unless it's damn near free) would I get a Cort - not a bad guitar, just bland.
You could get a fake Gibbo...but that really can be hit n miss - at best it's a rebadged epi with upgraded pups - at worst a badly made bodge job.
Distributors for Epiphone were Marshall/Mars - after thier spilt, I'm not sure - think Mars retained the dealership. PRS - no idea!
As a strat head, I have to mention that the S-type (Strat copy) guitar in HSS config is the more versatile, less back breaking guitar. More moddable too! And the last Yamaha Pacifica I played was too fun -But I digress.
Amp : Boss Katana 50w - New R4500
Guitar Epi/Tokai LP 2nd hand - +/- 4k-5k
Cables/Picks/etc - Remainder of budget.