Hi Andy, welcome to fishlore!

GBR's are lovely, they are also one of those fish that are very sensitive and will not live if stressed! This means you can not put them in a tank that is not fully cycled!
They are ph sensitive also, though if you acclimate them VERY slowly they do better.
PLEASE listen to Tom and Jacko, there are lots of lovely fish that will be completely suitable in your 10 gallon, and since you are on a tight budget it would be better to have happy healthy fish.
If you can go to a 20 gallon, it would be fine to get the GBR's, but read up on them, and make them the spotlight fish in the tank, with maybe only otoes and 3 corys as tank mates. If you then set the whole tank up with their needs in mind it would be a satisfying experience.