Let's separate this into conceptual issues + practical issues…
Avoid at all costs running the full load for a circuit through the switch that controls it. This usually involves 12V power being delivered to both a switch and a relay. Your load (the LEDs) attached to the normally-open contact on the relay's switched side, and your switch is connected to the control/coil side;
Fuses should be the first thing in any circuit;
The switch you choose should be a "latching" style device, not a "momentary" switch. A momentary switch/button will only complete a circuit while it is held down, whereas a latching switch holds the circuit in one state or the other. Current rating is not important, as your load will not pass through the switch (see #1);
Usually, power is siphoned from an existing fuse with a "fuse tap." These are not particularly elegant devices, but will accomplish what you want. Choose a circuit you know has extra capacity and isn't used for other essential functions;
Choose a fuse that is just above the maximum expected current draw for your entire LED arrangement;
Make sure the LED in your button is rated for 12V, or you'll burn it out pretty quickly;
I would recommend looking at some how-tos for aftermarket fog light installation—they operate on basically the same principle: a switch controlling a relay that turns the lights on and off. All your factory-installed lighting circuits are built like this, which is why you have multiple fuses + relays under the hood (and driver-side dash)!
You should use a relay to handle the load. This is one of the simplest ways I've found to wire in a relay. Uses the least amount of wire. If you wire it to the battery, add a fuse. If you wire it at the under hood fuse box, an Add-a-circuit is super easy. Wiring the switch from 85 to ground is also the safest because if any of it shorts out, it just turns the lights on instead of blowing fuses or melting wire.
Online Wire Size Calculators & Tables to find out what gauge wire for the light bar. That's from battery to 30, 87 to the lights, and lights to ground. That part of the circuit should be as short as possible. Jumping from 30 to 86, 85 to the switch, and switch to ground can be thin because it draws very little current.