Choosing a guitar is a pretty tough choice, I know. I have 6 or 7 and those are the best I have ever had. I’m not sure how guitar-savvy you are, but I can do my best to help you out.
From the genre that you're looking for (modern metal, classic rock) definitely stay away from Squier's, Starcaster's or any starter kit. They only last as long as a band-aid and soon you'll be dishing out a lot of money on strings, polish, cleaner, straps, picks, etc. Don’t put out more money than the guitar is worth, you know?
Ibanez’s are my favorite guitar company of all time. I have never been disappointed with them at all. Just got myself an electric-acoustic AE120 for Christmas and it’s amazing. Ibanez’s are entry-level guitars that are around the price range you’re looking at and provide the quality you need for metal/rock music. From top to bottom: the head stock is durable and grovers rarely get your guitar out of tune. Their necks are relatively thin and your fingers can glide across it. The body of the guitar is very light and sometimes you’ll forget you’re wearing it. Pickups are amazing; humbuckers are a good option when deciding on a guitar because they’ll give you that fat, raw tone you want. If you’re wanting one of them, try this. It was my very first electric guitar but I sold it to buy myself a Epiphone Les Paul, hah. The GRX20 is an amazing guitar with the kind of sound you’re looking for. If you want to dish out an extra $50 for a mash-up guitar made for both classic rock and metal, try the GART50FA. It has thicker humbuckers and more control over your EQ. Of course, you can definitely fin these babies used in shops around your place; might even find mine, hah.
Other options you should consider are Epiphone guitars. They’re the son of Gibson guitars, but they cost less and sound a lot better in my opinion. It’s like building a PC and going out and buying an Alienware, the brand name will make it cost more. One guitar that is definitely suited for you could be the SG. Amazing guitar and their stock pickups are nice. I replaced my Les Paul with Seymour Duncan Blackouts, and it sounds so good.
The most common guitar that you will see used and will be good for you are Telecasters, Stratocasters; basically any Fenders. You can never go wrong with a classic guitar, but getting them to be in your genre range is tough. I don’t think I’ve seen too many modern metal bands with a Strat, lol. You can get those really cheap though, and if you can get it cheap, you might have enough change up your electronics and give it the tone you want. I’ve never had a problem with a stratocaster, even though I use it for blues like Hendrix, John Mayer, etc.
So all in all, I would aim for an Ibanez or Epiphone, and I’m positive that you can find one of those used with a good price, but also try out a Strat in the mix and see how you like it. My decision point on choosing a guitar is how it feels on my hands and how much of a beating it can take. If I paid good money for her, then she better be able to handle my type of abuse.
Keep your options open and you are definitely heading in the right direction towards what you want.
I hope this is helpful and good luck with shopping!