Knowing WHAT to get is more than half the battle. My experience with a kit is tha the guitar was terrible and the amp worse. With what I know now, the guitar could have been repaired. You probably donāt wnt to deal with that on day one though.
At $500, you should be able to select pretty useful items, albeit possibly simple in terms of function. The Squire or Epiphone brands are ok and there are others. I bought a very satisfying amp and cabinet for <$150, but by the time I did that, I knew what I was doing much better than my initial guitar+amp kit purchase which was returned.
Donāt dismiss used gear. If it feels good and makes you want to pick it up and play, then it is a good candidate. You will get better gear out of your dollar finding a used guitar store and looking there over Amazon. You can also try before you commit money.
Consider a telecaster style. it is a popular sound for country and has certainly been used in rock.
Headphone amps are for you and you alone. You wonāt be sharing your sound with others (at least not without some fiddling to get it into speakers). A small practice amp is more versatile and you can always plug headphones to most of those. You can make that a must-have feature for your selection.
There is a lot of info buried in these:
guitar info seems to be a mixed set of personal preference lists. Maybe this video will be useful: