I'm going to take a contrarian view. Old people do that from time to time...
I see two potential goals here: Learn to play with plastic chips or learn a bit about logic and logic design. If the goal is to play with a lot of plastic, like maybe Ben Eater's CPU project, rock on. That's a great learning project. But it's a project, there's a goal. Just watching an AND gate work, well, you can pencil whip that and learn just as much. You can learn about DeMorgan's Theorem and Karnaugh Maps without ever actually seeing a piece of plastic.
The thing is, chip count is limited. A couple of dozen is a lot and I would think somewhere around 100 is a logistic limit. At least it was for me when I was doing this stuff with wire-wrap. So, a hundred chips with 4 gates per chip - about 400 gates equivalent. When I buy an FPGA, I get a million gate equivalents. Maybe more! And I get memory as well as a virtual dumpster full of logic. Wire-wrap is reduced to typing. My cut-strip-wrap gun is nowhere near as fast as my keyboard.
If you have any long-range purpose for learning about logic design, start with something that has a future. In my opinion, FPGA boards with lots of gadgets make sense. Switches, push-buttons, LEDs, 7-Segment displays, maybe a VGA port, etc. The gadgets make the board useful. With that in mind, I like ANY of the Digilent boards and, for the money, this is probably the best thing out there (remember, I want gadgets, bare boards are obviously cheaper):
https://store.digilentinc.com/basys-3-artix-7-fpga-trainer-board-recommended-for-introductory-users/Yes, you can do the beginner AND, OR, XOR stuff usig the switches and LEDs but getting started will be a little bit of a climb. There's plenty of help around here... Once you get used to dealing with Xilinx Vivado and programming your first blinking LED (The "Hello World" of the FPGA community), you will be on your way to an education in logic design without all the anguish of actually trying to push little pieces of wire into breadboards. I've done it and I'm not going to do it again.
While I'm on a tear, I going to put in a word for VHDLwhiz.com. He tends to use a really cheap Lattice IceStick:
https://www.latticesemi.com/icestickI have a couple of those and they are pretty neat - but slow and kind of small. Big enough for real projects though. I have to say, $25 for a development board is fairly cheap. But it is really short on gadgets and the Lattice toolchain (IceCube2 and Diamond Programmer) isn't anything I would write home about but it works and it's free.
Or just buy an assortment of chips. It doesn't matter which but I would suspect that 4000 CMOS is easiest to use. The Ben Eater project uses 74LSxx logic and that stuff is still available. The thing is, the kit of parts costs a LOT more than a decent FPGA board and, in fact, competes with my preferred board:
https://store.digilentinc.com/nexys-a7-fpga-trainer-board-recommended-for-ece-curriculum/So, a dozen breadboards with hundreds of connections or a couple of thousand lines of code. And the FPGA board is serially reusable. In seconds, if the project is already available as a bitmap.
Somebody has to take the contrarian view, so I did. Either way, have fun!