You need a phone with more storage (what the phone is wrongly calling memory). The Wifi should work all over a normal one story house, but if you're directly above or directly beneath the router, it may not work. (The radiation pattern from a router is sort of like a donut.)
Depending on what you want to store on the phone (apps or files) you may be able to add a 32GB microSD card. (Only for storing files - audio, video, pictures, documents, etc.) If you want to install more apps you'll have to get a phone with more internal storage.