If you have modern hardware, you can absolutely train that at home. Or very affordable on a cloud service.

I’ve seen a number of “DIY GPT-2” tutorials that target this sweet spot. You won’t get amazing results unless you want to leave a personal computer running for a number of hours/days and you have solid data to train on locally, but fine-tuning should be in the realm of normal hobbyists patience.

Not even on the edge. That's something you could train on a 2 GB GPU.

The general guidance I've used is that to train a model, you need an amount of RAM (or VRAM) equal to 8x the number of parameters, so a 0.125B model would need 1 GB of RAM to train.