It depends on what you mean by range and quality, but IMO there are really two important dimensions to drones: weight and video transmission.
On weight, the FAA has fairly strict rules for anything weighing above 250g. If you're just looking to have fun flying around your house or yard, I would stick below 250g. Otherwise you have to register the drone with the FAA, think carefully about where you fly, and broadcast a remote ID at all times.
For video transmission, "analog" video transmission is typically cheaper and has lower latency, but is fairly low visual quality (it looks like watching a VHS tape on a small screen). Analog is certainly good enough for flying around your yard or house, but can make it hard to see some details (like small sticks/branches) and is not generally good enough for taking shots of scenery. Digital is the other video transmission option, which is where you get entrants like DJI that offer extremely crisp video but are more expensive and you get locked into the DJI ecosystem (have to buy their hardware, including video systems and goggles). For getting started I would pick analog and upgrade to digital if you enjoy the hobby.
For someone just looking to get started flying around, I would start with a tinywhoop like an air75[0] (which broadcasts in analog), some entry-level analog goggles [1], and an entry-level radio [2]. It may not be pretty and you won't be able to fly far, but you'll get a feel for how to fly and then you can upgrade piecemeal as you figure things out.
Regarding:
> that going the custom route could yield better results for less money than just buying something like a DJI mini straight away?
Unless you really like to tinker, I would start with getting an off-the-shelf drone. A DJI Mini is a great drone depending on what you want to do. Minis are good for aerial photography and coasting around, but not so good for acrobatics or fast flying / racing. Plus it'll be more expensive than the options I outlined above.
[0] https://betafpv.com/collections/all-drone/products/air75-ii-...
[1] https://www.amazon.com/Goggles-800x480-Diversity-Headset-200...
[2] https://radiomasterrc.com/collections/pocket-radio/products/...