For driving unipolar stepper motors I’ve used ULN2003 chip. 7 Darlington transistors with built in flyback diodes on one 16 pin chip. Much easier than using separate FET or transistor. Handles 500mA which is plenty for driving a slave clock
For bipolar (4 wire) motors I’ve used dual H bridge chip. When my PC problem is fixed I’ll be able to look up the number.
I’m sure there are Arduino libraries for doing t, but I wrote my own using bit twiddling on PortB.
The 48 step motor I used in my slave clock came with a 15t cog, which looked a bit difficult to get off, so I meshed it with a 75t gear on the minute shaft and advance once per 15 seconds. Then I got ‘clever’ and advanced it 4 steps every minute, why, just because I could.
As far as using electromagnets and ratchets, that’s what Gents and Synchronome slaves do, the noise isn’t too bad, quite a feature in fact