Trying to get a phone to replace my brother's Samsung Galaxy Nexus:

Brand : Any Android brand
Spec : Not too much bloatware
Budget : 500 (can over a bit)
Size : 4" -ish

Also, getting first smartphone for parents:

Brand : Any Android brand
Spec : Not too much bloatware, simple UI
Budget : 500 (can over a bit)
Size : 4" -ish