How to wire additional relay for heavier load
Just stick to electromechanical relays for simplicity.

Use your little relay to drive the coil of an even bigger relay. Don't parallel both relays' main contacts so they share the load since you can't guarantee they switch at the same time. 







simulate this circuit &ndash; Schematic created using CircuitLab

If a relay has two pins it's probably a reed switch where applying a nearby magnetic field closes the contacts inside. This means that the magnetic field is the control signal and the two pins are for the load. You don't want this.

Relays should have a minimum of 4 pins. Two for the coil (control signal) and two for the primary contacts (main load).

If a relay has 5 contacts it means that two are for the coil just like before, and the three remaining pins are for the load. They are the common, normally open, and normally closed. When the coil is unpowered, the common is electrically connected to the normally closed terminal and disconnected from the the normally open contact. When the coil is powered, the common is electrically connected to the normally open contact and disconnected from the normally closed contact.

If the relay has more than 5 contacts it might be switching multiple electrical paths simultaneously.

There are also latching relays that have springs which hold the primary contact in the current position even if the coil is unpowered.

It is most convenient to pick a relay that has a coil voltage rated for the voltage you intend to drive it with. But the current is what really switches the relay. 

The coil has a resistance and a required current and the voltage that can drive that current through the resistance is what ends up being the voltage rating for the coil. If you want to apply a voltage that is higher, then you just need to add more resistance externally.

So if your coil voltage rating matches your applied voltage you can connect it up directly since the coil's inate resistance is able to limit the current being pushed by the applied voltage at a safe, but usable level. But you can always connect a HIGHER voltage than what the coil than what is rated if you add in a properly sized series resistor to limit the current at what the coil operates at so the coil does not burn out.

Note that it's harder on a relay to switch DC than it is to switch AC. When the contacts open an arc is made (especially if it's interrupting current to an inductance like a coil or motor). The AC sinusoid naturally crosses zero which self-extinguihses the spark. DC does not.