Low power always ON storage / nas server for home

Hi, in my home, there always 5-6 devices including phone and laptop using network (wifi), time time I have been situation where we need to transfer files from one device to another. Currently we use a desktop to server as storage. But I don't want to always go and turn on for even small file transfer and on the other hand want to save electricity too. So am planning to have something custom , tiny to which I can connect 2TB or more HDD, have WIFI inbuilt and support for RJ45, thats pretty I need. I can think of raspberry pi B+ but again , making something useful out of it need lots of tinkering and more stuff like case, power supply etc. Then if I search online, can find lots of small android PC (2GB ram, quad core ) in price range of 5K to 10K but not sure how to attach hdd in them, through USB . Can they provide enough power to power USB hdd ?

Any suggestions ...