Suitable electronic components and digital logic gates for simple application
Your main difficulty will be protection of the logic components against ESD and overload.

My first thought was to suggest something like LS as being more robust than HC, but it's not immune to ESD, and being TTL uses asymmetric thresholds, has significant bias currents and a tight VCC range, which make it less than ideal for the neophyte.

With a few extra components, HC can be made fairly bomb-proof, and as it's specified from 2v to 6v, it would allow an unregulated 2 or 3 cell alkaline power supply (4 cell even, abs max is 7v) to be used. I'm thinking a diode clamp pair on every module pin exposed to the user, with 200 ohm series to the IC outputs, and 10k series to the IC inputs. That gives ESD protection two bites at the cherry, and allows LEDs to be connected directly to outputs if you want. Don't forget VCC capacitors.

How instructional and how representative do you want these to be? Do you put a 1M pulldown on every input? Yes if you want them to 'just work' with inputs left open, no if you want them to find out the hard way about leaving CMOS inputs floating. I think I've just persuaded myself into recommending pulldowns, as some logic families can legally leave inputs open, CMOS will draw excessive power when oscillating, you're not necessarily teaching them CMOS but generic logic, and you can specify in your book of words that 'this logic defaults to LOW when unconnected' (or HIGH, or active or inactive (think which you need from a didactic point of view)). 

To expand on the didactic use of default inputs, if you provided (say) a 4 input AND gate, and defaulted the inputs HIGH, then it would work as a buffer, or a 2, 3 or 4 input gate by just connecting the inputs you needed, while leaving the others open. 

Continuing with didactic considerations, what logic functions do you want to provide? While learning logic, I was always thrown by NAND gates, 'why do they have to provide the complement, what's wrong with an AND gate?' Because it's simpler inside, a NAND uses less power and is faster than an AND, which is why you'd choose those for a real design. But is it the right thing to choose for neophytes?

You can get single gate per package CMOS logic in SOT23-5, or 4 gates per package in SO-14 or DIP-14. Fairchild's Tiny Logic (HS family === HC) or the Little Logic from Texas (AHC === HC) give you single gates equivalent to HC, though the abs max is lower at 5.5v.

You might want to consider that if you made a single board that took a quad NAND 74HC00, you could configure it to be a NAND, AND, OR, NOR, Inverter and even a 2:1 multiplexer, by cutting tracks or solder-blobbing links on the board, if you wanted to minimise the number of different parts you used. Unfortunately, a quad NAND won't give you an XOR, you need 5 NANDs for that, so just use an 74HC86. But that's just me being old skool. As CL points out in comments, the Texas 74LVC1G199 'ultra configurable' gate does all of those, with Schmidt inputs, so maybe that's your one part. 

Schmidts are useful for delays, essential for clocked logic if you want to go there. This is specified to behave itself when input voltages are not clean logic levels, allowing it to be used after timing RC delays, as an oscillator, and for switch de-bounce. Plain switches give multiple transistions, de-bounce is essential if you want to clock them manually.