Since I've never owned a p300, I'm not sure exactly how it works, but it certainly should be used while plugged in whenever possible. This will give you the maximum brightness it offers, and should have no problem giving you a 100" to 120" diagonal if you want to go that large... after dark of course.
I've even looked at projectors which can use high powered USB charges to run them, but those are far too dim at this point to be something I would recommend.
Look for reviews out there of the p300. Be aware that it is a 720p projector, not a 1080p projector, which saves you some money, but will decrease resolution a bit. Not a big deal if you are just having fun with it. But, the image itself should look very good. The size should be excellent for travel use.