What You'll Need
Initially, the tools you'll need will be minimal for the prototype construction on solderless breadboards. An oscilloscope is useful to have, but you can get by with a logic probe. A multimeter is always good to have on hand, though I don't call for it specifically in my instructions.
A device programmer that supports the Dallas DS1225 non-volatile RAM chip is also useful to have, but the IC can be programmed in other ways, as well. For the short programs used in the initial testing of the system, the RAM can be programmed by hand on a breadboard setup. Before long, however, the software starts getting longer and either a commercial or home-built device programmer will be needed. The programmer does not need to be complex. There are many projects on the 'net for interfacing a PC directly to a RAM that can be used to dump programs onto the NOVRAM.
I suggest getting something in the way of a programmer and testing it before starting the MAG-85. Programmers that support standard 28-pin 8Kx8 RAMs of any type should work, since the DS1225 uses a standard RAM pinout. So even programmers that do not explicitly support the 1225 will usually work.
Finally, I strongly recommend getting a chip pin straightener. It makes using new or recovered chips much easier and nicer. Most of my chips are pulls from old scrapped boards. Not all of them were pulled out of the old PCBs gently. The pin straightener earns its keep with all my projects. Make sure you get one that handles both 0.3" ICs as well as 0.5" ones.
Regulated Power Supply
A well regulated power supply is crucial to putting together a new system. Once the system is known to be working, it can be moved to another power system, like battery power or an AC adapter. But, during construction and testing of the system it's essential to have a good 5VDC supply. That way you don't end up wondering if the problem is the circuit or the power supply, or thinking that your circuit or chips are no good when it's just power supply ripple driving you crazy.
I built my system on an HP logic lab, initially, to get a good DC power supply. Other similar labs will work as well, or a PC power supply can be modified to act as a well-regulated bench power supply. I don't give instructions on how to do that here, but there are plenty of other places that detail doing that.
You'll want enough solderless breadboard space for about 12-14 integrated circuits, including some 40 pin and 28 pin ICs. I not only use my logic lab's breadboard area, but loose solderless breadboards for peripherals like the LCD display and keypad.
It's also nice to have a zero insertion force socket for your memory chip. It's not at all critical, but you end up worrying a lot less about whether you've bent a pin while swapping out memories during development. They're not cheap (mine is the most expensive part of my system), but I find them worth it, even when building on solderless breadboards.
Plenty of Chips
I try to have at least two of each IC I'll need on hand. That way, I have an extra in case I fry one. For this project, I've found it helpful to have multiple memory chips (Dallas DS1225's) on hand as well. This allows me to have not only one for my current system software, but extras with different test programs. That way, if something starts acting odd I can put in an old program and see if I've messed up the hardware somehow.
Having spare parts also means that you can leave your breadboarded system alone while building up the permanent version of the system. Then, if something doesn't seem to work in the permanent build, you can use the breadboard system as a reference to see what's different.
Long Term Plans
Once the prototype system is complete, you'll want to make a permanent version. That may be as simple as screwing the solderless breadboards to a backboard and shoving the whole thing into a case, or it may be a wire-wrapped or soldered system. At present, my design does not include a printed circuit board. So plan ahead while you're constructing the prototype by figuring out what you want your MAG-85 to be long term, and start collecting the appropriate pieces of hardware.
A small, simple system is nice in many ways, including the fact that you can do so many interesting things with it. Build it up in a peanut butter jar. Convert an old adding machine into a microprocessor system. Put it into a cigar box.
Then there's the keypad. You can get keyswitches out of broken PC keyboards, or use subminiature pushbuttons available for pennies apiece. Maybe construct your own membrane keyboard out of copper stock and cardboard.