Mechanical Keyboards
Believe it or not, this is actually a hobby! Mechanical keyboards are keyboards that have a mechanical switch for each key rather than a rubber mat with bubbles on it. You can customize pretty much every aspect of these keyboards if you get the right one, with some people even making their own from scratch!
The Board
First, you need a circuit board. I'm including the case, switch plate, and mounting system in this section as well because I've never customized those myself and most entry-level options will have all 3 parts. If you don't know how to solder, you want something called a hotswap keyboard. Look for one with 5 holes for each switch. The boards that I have are the RK ROYAL KLUDGE R75, the Epomaker TH80 (I think, this is the closest I could find), and the original GMMK (the latest version is linked). This is usually where the bulk of the cost lies: the latest GMMK costs $270 without any keycaps or switches. However, the entire R75 cost $60, so you can definitely start with a cheaper option.
Direction
First, you need to consider whether you want your switches north-facing or south-facing. For most people, it doesn't actually matter. However if you want RGB to shine through the legends (letters) of your keycaps, you'll want north-facing, because the LEDs will be at the top of the key. If you want to use keycaps labeled "cherry" profile, you'll want south-facing, because the keycap will hit the switch before it's pressed all the way sometimes if it's north-facing. For me, it's a bit of a non-issue as I don't care about either of these. The TH80 is south-facing and the others are north-facing
Case Material
Case material choice is all about sound. The keyboard will usually sound deeper and more resonant if the case is metal, especially the bottom. Metal also makes it look fancier.
Mounting
I don't know as much about mounting systems, since I can't customize them on any of the boards I have. The latest GMMK has gasket-mounting and offers two options for different amounts of flexiblity. If you pick a more flexible mounting system, the keyboard flexes when you type, which is apparently good if you type for long periods of time. I use my keyboard mostly for gaming though, so I prefer a stiffer keyboard.
Switch plate
The switch plate is the layer that sits between the edges of the switches and the circuit board. Different material provide different sound profiles and flexibilities, with metal being better for sound and plastic being more flexible. Some switch plates will even have slits cut into them to make them more flexible, but those are usually only seen on high-end hobbyist boards.
The Switches
The switches are my favorite part of the keyboard to customize. Different switches have different sounds and feel different under your fingers.