We get the Lumia 635 as a pool phone at work. The battery life is nice, the windows phone stuff is a bit meh. No idea if the selection of apps is any good. I did see an old geezer using one of the bookie’s apps in the pubs the other day, so it might be more relevant than you’d think. I find the keyboard frustrating – not sure if you can get Swiftkey for it. Otherwise, it’s alright.
The cheaper Galaxy phones are usually a bit sluggish.
I would suggest getting something like a second hand Galaxy S3 or iPhone that hasn’t been updated to the new iOS would be more sensible than getting a dirt cheap new smartphone. My Mum had a series of slow as **** phones which she could never get used to. Which isn’t really surprising when there’s several seconds lag between each button press / screen tap and the actual result. Makes it almost impossible to work out what’s going on.