Either one will work for that project. Personally, I hate changing batteries, so I'd go with a plug-in adapter. The one in the store a lot more power you need. Too much power is not going to be a problem. But look around, you may have a 12v wall-wart lying around. Just be sure it is a DC regulated one.
If you choose an adapter with a barrel plug, one of these adapters
will simplify the wiring a bit.