[Solved] When should I use a transistor, mosfet, and when should I use a relay?

Anonymous Penguin Asks: When should I use a transistor, mosfet, and when should I use a relay?
I am used to relays some, and they are useful, especially for large loads like a incandescent light bulb or other 120V AC device. However, it seems like overkill to use a relay for a bunch of LEDs linked together (parallel) that use 60 mA (too much for the Arduino). Also, it wouldn’t work if you wanted to turn it on/off frequently or do PWM. I’ve heard some about transistors and MOSFETS and know a little about them. When should I use each one and how do I know what type to get? Also, it seems like relays can be more expensive than transistors/MOSFETS.

Edit: How can I use these with my Arduino?

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