Best digital camera for the money?

I have lately had Fujifilm brand cameras. My Z70 has a black spot on the screen, but works. I think its probably time for another. I had an Olympus years ago, but it broke not too long after buying it. My mom has a Fuji SLR that is nice, but I can't afford one of those. My father in law has a Canon Rebel, we can't afford that either. I found a nice Fuji called AX550 that looks nice, are these any good? We are expecting our 2nd baby next month and color/picture quality is our main concern. Battery life is also a big concern. $85 or below is our budget. What kind of camera is good? My mom is on her 2nd Z100 from Fuji and loves them. Any tips on getting a good camera?

The Canon Rebel t4i at $800.