I accidentally posted anonymously, so here's what I wrote, and what I want to add to:
Well, if you want to tinker with 1970s-era home computer technology, the parts for doing so still exist. One of my builds had a Zilog Z80 processor, 32kB of SRAM and EEPROM memory (no interface circuitry required), plus a 4 MHz clock generator. For output, I had 2 latch DACs and a latch gate, hooked up to the X, Y and Z (intensity) inputs of an oscilloscope. Plotting vectors on the screen every 20 or 40 ms only takes up a few processor cycles. Input from a PS/2 keyboard runs at such a low baud rate that you don't really need to worry about having a chip for it either. Use a simple multiplexer and a couple of logical gate chips to set up interrupt triggers for the screen refresh and keyboard input. I believe the PS/2 has a clock pin, so just trigger when that's high or low. You could hook up your EEPROM so the processor can flash it, for some primitive storage, or you could hook up an old tape deck to some simple analog circuitry, for Commodore 64-style storage. IBM PC floppy drives also use a very simple interface, but you'd need more logical circuitry. You could toss on another Z80 as an I/O co-processor and run them in lockstep with the 4 MHz clock. The possibilities for fun tinkering are endless.
I must admit that I've had trouble finding an easy, inexpensive way of prototyping. Sending PCB layouts to fabs is a little bit expensive, especially if you make a mistake. I've used veroboard in the past, but all the soldering for bus lines can take its toll on the copper tracks, especially if you make mistakes, and you often end up having to throw out a board after a while. I've been tempted to try wirewrapping tools lately, because of how easy it is to fix a mispatched connection. I have also experimented with laser printer etching, but it's time consuming, and the chemical brew you need for it is rather nasty. The closest thing I have gotten to "real time development" in the way you would do with software is SPICE, specifically LTspice in my case, but you have to watch out for some things. In the simulation, conductors are ideal and have no time delay, resistance or capacitance, and components behave perfectly, with no thermal noise, so you risk doing an entire design in SPICE, and then discovering later that you actually needed those seemingly optional decoupling capacitors for the circuit to remain stable. This becomes especially apparent as you get closer to the gigahertz range (and is part of the reason why circuits have kept shrinking over the years, as this reduces those side effects).