Choosing a switching device
Almost definitely a MOSFET. The only issue really is what voltage is available to drive it.

Let's say you have a 15V battery with a 5V on/off signal referenced to battery negative. If your load can float and can attach directly to the battery positive, then you can use an N-channel MOSFET: tie MOSFET source to battery negative, drain to the side of the load not connected to the battery, and the gate to the on/off signal through a small (50-200 ohm) resistor.

If the load needs to be grounded, you need to use a P-channel MOSFET with drain tied to the ungrounded end of the load, the source tied to battery positive, and the gate drive circuit may be a little more complicated (* = I might post details later).

A 15V battery is small enough that you can get away with a MOSFET rated for 25-40V range and there are super-low on-resistances that can handle 60A loads.

edit: you don't say what kind of packaging you are looking for. If you are planning on using a circuit board for other things, go with a MOSFET in an SO8, DPAK, or D2PAK package. SO8 sounds iffy for 60A loads unless it's for a really brief time, but it's probably the most cost-effective, though the worst for thermal dissipation. DPAK and D2PAK are beefier.

If you're not planning on using a circuit board, an automotive relay would probably be much easier to use.