These statements don't exist simultaneously. The amplifiers I've ran for the past 25 years started at $1k each for just the amp. Same budget for speakers. Same budget for subs. And I would say that I am concerned with price. In my '23 1SS I'll run a Hertz Mille 3-way and Hertz Mille sub on two JL VXi amps - so about $6k in gear.
A few hundred isn't precise enough to have a conversation on what to use. $300? $600? Is that the price installed or just equipment? Install will certainly be "a few hundred" with a prefab box. Are you thinking about a prefab sub box or a custom box - custom is obviously more expensive but you save trunk space when done properly.
You can buy a cheap amp (under $200) and cheap subs (under $100 ea.), but they won't last if you push them. If you run them within their limits, they can last a decade. You can buy used and save a ton of money, but there are always risks. I have no issue with used gear, and I own a ton of it, but maybe 5% were worse than expected.
Vented boxes help boost output but then you must set the subsonic filter correctly or you'll destroy the subs. Vented boxes also take up more space. It's a decision you need to make when you make gear selections.
Install costs needs to include getting a signal from the factory amplifier, from the front speaker outputs. The amplifier should have high-level, balanced inputs to accept this signal directly. Otherwise, you'll need an interface, like an Audio Control LC2i, to adapt the factory output into a low level signal (you also gain an auto turn-on).
If you visit car audio specific forums, they can offer generic advice, but they will tell you to come here for vehicle-specific advice. We have an audio sub-section on this forum where this post should be moved.
https://www.camaro6.com/forums/forumdisplay.php?f=228