Does the $100 include a receiver and screen / goggles, or is that just for the equipment going on the car? I feel obligated to point out that if you're just trying out PFV for fun and don't want to spend a lot on something you may not continue to pursue, that's completely fine and it's how I started back in the day, but from personal experience if you decide to stick with it you will need to re-buy nicer versions of everything later on.

If you want a halfway decent set of goggles, like the EV800ds that are often recommended here, it'll eat up the majority of your budget, but although quad pilots usually avoid them there are cheaper options out there that should work on a car, albeit at the expense of some range, signal quality, and/or latency. If you've already got a portable monitor you could pick up one of the older-style non-diversity RXes to connect to it for a couple bucks. If you don't have a monitor you could go the phone + UVC receiver route (higher latency), or get an integrated battery-powered screen + VRX combo.

For transmitters, I see a lot of stuff on Amazon from AKK, which is a brand I've used in the past and which seems to work fairly well while still being rather inexpensive. They've got a 1W analog VTX with integrated SD card DVR, mic for recording sound, regulated voltage output for a camera, and button to configure band/channel/power so you don't need to worry about smart audio. There are analog VTXes on there that list higher transmit powers, but just be aware of exaggerated claims and remember that to get double the range you need 4x the power, not 2x. Honestly if there are no special features you want I'd just pick one with good reviews.

You should be able to pair the above with basically any analog FPV camera that can run off 5V if you intend to power it off the VTX output; just get one rated appropriately if you plan to power it off the LiPo directly. The Caddx Ant is a well-known camera in the FPV world that seems to be available fairly cheap on Amazon. If the camera will be exposed and you're concerned about it getting wet or dirty, you could conformal coat the board or just get a model that's got a more substantial case. There are plenty of other cameras on there for less that look like they should work, but with all the re-branded white-label stuff on Amazon it's hard to know what you're really getting.

Last but not least, you may want to get some additional/better antennas. Some transmitters and receivers come with antennas, some don't, and the ones that do won't always have the same polarization. For example, the AKK VTX I mentioned does not come with any, while all of the receivers I listed come with linear antennas. If you plan on driving around in largely open space, linear antennas should be fine and you can pick up some more cheap ones for the VTX. If you plan on driving in places with obstacles the signal may bounce off of, you'd probably want to get some circularly polarized ones that'll reject multipath interference a bit better. Any equipment that comes with lollipop or clover antennas will also be circularly polarized, but make sure that you pay attention to right/left handed and make sure all your stuff matches. Also be careful not to mess up SMA and RP-SMA, etc.