I don't have a Raspberry Pi 3, but noticed that it says it needs a 2.5A power supply. I have a lot of the cheap <1A chargers at home. Can these power the Raspberry Pi 3? Also I guess I won't be able to power it with my regular USB ports from my computer?
The Pi3 does not NEED a 2.5A supply, although this is recommended.
I can run mine from an Apple 5W (1A) supply quite happily.
It all depends what you want to do with the Pi.
You would not be able to run lots of peripherals, although a USB keyboard and mouse are OK.
I would be wary of cheap USB supplies. Many of these have very poor voltage regulation. Provided the red light is on and REMAINS lit you should be OK. The GUI has an indicator which comes up in the top right if the power is inadequate.
As an electronics engineer, I can tell you that a 2A-5V adapter will not affect your Pi in a bad way.
Imagine that the voltage is pressure and the current is a rope. If you increase the pressure; i.e voltage in this case; your Pi will be burnt. If the current is less than the required the rope will be stretched to its max and get cut.
Fortunately, the Pi has short-circuit protection so when the rope is cut; i.e the current is insufficient; the Pi shuts down automatically to protect it from getting damaged.
If you connect more than 2 USB dongles in the Pi, I recommend you use the 2A-5V adapter, as the peripherals are current hungry and will try to get sufficient current to operate, or as a result the Pi will shutdown automatically as I mentioned before.
If you try to use the Pi with WindowsIoT with the 1A-5V power supply and 2 USB dongles are inserted in the Pi, it won't boot and you will get stuck in a reboot loop, and the SD card might get corrupt in this case.
My father is an electrical Engineer he said it won't effect if you used 2 A / 5 V, but the temperature will be high a bit.