If you make a HDD external with an "Enclosure", then it will be USB interface. Depending on your computer, you can boot from the USB HDD and use it as a regular internal HDD.
And yes, most enclosures come with a powersupply. There will be a power button and a power LED light on the enclosure.
Making an internal HDD to external used to be cheaper but I've noticed price cuts for external HDD also so it's your choice. Both should work in the same way.
Lastly, if you planning to buy enclosure for an internal HDD, make sure you buy the right enclosure. Enclosures are different for Serial ATA and IDE hard-drives.