Small Vibrating Motor at Set Intervals
Microcontrollers

The canonical answer for this type of question seems to be that you should look into using a small microcontroller. You can get PIC and AVR microcontrollers that are no bigger than a 555 timer.

As a hobbyist with a low level of knowledge and skill, I find an easy way to find example circuits to use as inspirations is to, for example, google "avr led blinker" - because blinking LEDs is popular and not too far removed from driving a small pager motor.

That leads to interesting stuff like 


AVR ATtiny10 runs LED blinker for 6 months


I might start with an Arduino and shrinkify it to a 8-pin DIL AVR ATtiny before using SMT ATtiny. Other people would prefer to use PICs (some PICs are really tiny and ideal for wristband products)

I'd maybe have one pushbutton that cycles through the interval settings and maybe an extra LED for feedback e.g. 1 blink when set to 15m 2 blink when set to 20m 3 blinks when set to random. I'd try driving the pager motor via a BJT or FET. That means you need a microcontroller with one input and two output pins. Or you could use that pager motor for feedback instead of the LED.

555s

The "traditional" answer :-) is to use a 555. I'd use the same technique of looking for existing examples and adapting them. I'd start at somewhere like


50 555 circuits


Any circuit I concocted with a 555 would be likely to use a lot more components and a more complex circuit diagram and PCB layout than a microcontroller based solution. However you avoid the need to write software (I don't see this as much of an advantage).

BJTs

In principle, anything you can do with 555s you can do with small-signal generic jellybean BJTs (Google TUP TUN DUG DUS)


200 transistor circuits


Valves

You're on your own.

Next

I would try concoct a circuit based on ideas like that and come back here when I hit specific problems with the circuit