What size/type of circuit breaker do I need?

[ezdays]

Seeing that your transformer is rated at 3A, you should use a circuit breaker rated at somewhat less, like 2.5A @ 120v, and put it on the input side of the transformer.
145 feet of track is quite a load. In order to avoid severe power drops, you should place your control in the center (+/-) of the loop and run several power feeds radially from it to the track.

Good luck..!!

That transformer's 3 Amp rating is for the secondary, the input will be around a tenth that at full load. I would recommend putting the breaker in the secondary circuit just to protect the transformer windings should there be a short on the load side. A 2.5A breaker will do, but I'd also try to calculate the load before selecting a value. The 2.5A would definitely protect the transformer regardless.