Really what you need to do is get to a guitar store and try out different instruments, and buy the one that appeals to you most in looks, feel, and tone. No one guitar is the best, they're just different and different people have their preferences - chunky or slim necks, lightweight or heavy and solid, humbuckers or single-coil pickups, curved or flat fretboards, etc. Around the $300 price point, I would look at Squier's Vintage Modified and Classic Vibe series. There are quite a few versions of classic Fender designs in those series and they are well-made.
If you like a Les Paul, try an Epiphone. I'm also very fond of Godin as a company, though they're a bit hard to find in stores. I only have one electric (I'm more of a bassist), and it's a Godin Session Custom, which has a telecaster-style body but contoured, one humbucker at the neck and a single-coil at the bridge.
Lots of flexibility of tones (desirable when you're going to just use one guitar) and great build quality. That's more of a $600 or $700 guitar. But really, go try some out and just see what you like.
As for an amp, again, what's your budget, and where will you be playing? If you're going to be in a band where you have to be heard over a drummer, you need at least 15 or 20 watts through a 12" speaker or maybe two of them. Most feel that tube amps are best for tone, but solid state will get you more power cheaper.
For tube combos, a Fender Blues Jr. will do the trick for a little over $500 new, you can often find them around $300-350 used. I have an Egnater Tweaker which costs about the same. If this is just for playing at home, there are lots of solid-state amps with digital effects that you can get for around $100-150.
I like the ones from Orange, which are more intuitive to me without messing with presets and stuff. If you want tube tone in a home practice amp, check out the Blackstar HT-1 or -1r. Just one watt of tube tone, and they sound great.
But they cost something like $250 or $300 new.
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