There will be a brake line pressure sensor somewhere in your system, probably close to (If not on) the master cylinder. The sensor will be cheap, the fitting should be 10 seconds. However, it's advisable to:

- get the brake fluid changed and the system bled
- have the brakes tested on a rig after replacement
- make sure all of your brake pads (front and rear) are OK

... which will cost according to the garage's hourly rate. The job should not be much more than about 1.5 hours altogether. Brake pads will depend on your model and manufacturer, but for my Renault I paid E55 per front brake and E 38 per rear (about E 190, or $170) for a set of pads that I fitted myself.

I think in any case it's worth paying the garage the fee to have a brake test done, which should be no more than 0.5 hours (max) and they should be able to plug into the ABS system and find out why it's apparently kicking in at relatively low braking effort/pressures. It sounds like a sensor defect to me.