You said $200-$250. That guitar's $200. Tack on a cheap strap, tuner, capo, and pack of strings, and it should land you at $250. *shrug*
You can't get much cheaper, new, without getting a much worse instrument. About the only one I'd consider is the Fender CD-60S, at $150. Anything less, and you're looking at instruments with laminate tops and crap workmanship.
If you're willing to do some research and take a risk, used can shave a fair bit off. A used FG800 in good condition runs ~$140; an FG700, ~$120. Used guitar markets can be very seasonal, and what stores have in stock will vary week to week.
Squier Affinities are pretty bad, and the pack-in amp is pretty much valueless.
Electrics that won't hurt you more than help you are pretty sparse below $250(new). The cheaper you go, the more things are probably wrong with them, the more they'll negatively impact your learning curve, and the more you'll have to spend to get them fixed.
Again, at that price point, I'd end up pushing Yamaha on a value-for-money basis. The Yamaha Pacifica PAC112J runs $200. The PAC012DLX shaves that down to $180, at the price of a lower grade of wood in the body. One nice thing is that, since they're seen as beginner's guitars, they end up super-cheap on the used market -- the 112J typically around $120, and the 012 at $100 or less.
For the amp, I'd go with any used solid-state or modelling amp in the $50-$100 range. You'll definitely end up replacing it, so don't get too hung up on it. There's probably no shortage of options within driving distance. (For example: a quick online search of just Guitar Centers and Music-Go-Rounds near me shows a Fender Mustang I v2, a Peavey Vypyr VIP1, an Orange Crush 20RT, a couple Fender G-DEC Junior, and a couple plausible Roland Cubes. If I bothered to check Craigslist or other local guitar shops, I'd probably find a couple Blackstar and Vox modellers, as well.)
Remember: a good player can make music with anything.
And don't forget that Anderton's is -- first, foremost, and always -- a music store. Their Youtube channel exists solely to sell you shit. Despite this, I still like them...
Also, while it's a poor craftsman who blames his tools, it's hard to become a good craftsman with hands full of splinters. And I've seen cheap guitars which came from the factory with fret ends so poorly dressed they draw blood.
