Agreed about the power-on reset. The power-up state of a flip-flop, unless it has an internal reset circuit, will essentially be random as it depends on which of two logic gates can affect the other one, before being affected by the other one:

You can use a "microprocessor reset" IC to generate a short "logic low" pulse at power-on to reset your flip-flops, but for learning purposes here's how you can build a simple one yourself:

This uses an RC circuit to pull the /RESET signal low for a while when the circuit is first turned on. R2 makes sure that when the power is off, C1 is fully discharged. When power (VCC) is turned on, R1 will slowly charge up C1. Until the C1 voltage reaches about 2.1V (~0.7V Q1 Vbe + ~0.7V D1 Vf + ~0.7V D2 Vf), Q1 will be off and so Q2 will be on, producing a low output which resets the clock. After the C1 voltage is above the ~2.1V threshold, Q1 will turn on and Q2 will turn off, producing a high output and the clock will work normally. Q2 and R5 are basically just a logic inverter, so if you have a spare inverter in your circuit you can use that instead.
Just wire in two small push-buttons to manually advance the “hours” counter and “minutes” counter. (Seconds too, if you want to be anal about it, lol)
Agree with this too, although you'll want to debounce your pushbuttons. Normal digital logic can react to Mhz-range signals, and the contact bounce that switches produce can appear as multiple pulses to your circuit (for example, you press the "hours" button once, but it increments the hours 5 times instead of 1). You can de-bounce your switches slowing down the response time, by adding an RC circuit + Schmitt trigger comparator/logic gate to filter out the bouncing (start with ~100 ms RC time constant; the Schmitt trigger input is important because many logic gates are not happy with a slowly-changing input voltage from the RC circuit). You can also de-bounce your buttons in a bulletproof but more complicated way that doesn't rely on timing by using an SPDT switch like method #1 on
this page.