Different bulbs with different voltage ratings in the same (DC) circuit
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The answer depends on what the &quot;bulbs&quot; are. The two common ones are incandescent and LEDs. For either, you need more information to understand how to design the circuit.
Incandescent bulbs are basically resistors themselves and are rated by wattage (i.e., how much heat they can dissipate safely without reaching thermal meltdown and blowing up when you plug them in). So when you design your circuit, you can draw those bulbs as resistors themselves and calculate the current through them to make sure you don't exceed the allowed wattage (P=IV). You also need to know what the bulbs' resistance is, which would be the voltage they gave you squared divided by the rated wattage (since P=IV and V=IR). They can be parallel or series, as long as you follow those rules and draw your circuit well. The brightness will be a function of power, so calculating power is important if you want them equally bright.
LEDs work differently. They are diodes, and the voltage they give you is the minimum voltage you need to turn them on. They also should tell you the maximum current they can take before the blow up. You can wire them up either in parallel or series, but the brightness will be based on the amount of current following through the diode. Additionally, each LED's requires a different amount of current to reach the same brightness. So if you put them in series, they will all have different brightnesses since they will all have the same current. If they are in parallel, you have the ability to individually control brightness since each parallel branch can have a different amount of current. So, for LEDs, the most common thing to do is to wire all three in parallel. In series with each individual LED, you place a resistor to limit the amount of current through that particular LED (to control the brightness and to protect it from blowing up). Each LED will likely have a different resistor value in series with it, and sometimes the datasheet of the LED suggests how big it should be, but you can calculate it based on the equation R=(Vbattery-Vdiode)/I). One final note about LEDs, the polarity matters. The long leg goes to the positive terminal of the battery. That's because LEDs are light emitting diodes.