Firstly, regarding the upgrades.
Using the HD7850, instead of HD6850 would give an average increase in frame rates of around 40%
Using i5, instead of i3, is more complicated. Things which use multiple cores, like photography, certainly benefit. Multi-tasking will be less slowed. In many other ways, the difference is minor. Gaming will benefit, a bit, but difficult to quantify. In some games maybe 10%, in others, a bit more.
The motherboard is a reasonable budget Z77. As you are not overclocking the processor, you don't need a full Z77. It may be worth using ASRock's Z75 motherboard. They only do one, and it's not bad. About £75, on Amazon. You save £25 towards better GPU, and don't loose anything useful.
I don't see a power supply. You need something around 500W. Seasonic, XFX, and Corsair are good makes. Seagate Barracuda are better for hard drive (or WD Caviar BLUE or BLACK)
The PSU is the important thing to get right. A failing PSU can take the rest of your components with it. Good manufacturer, at least 80 Plus certified, modular (if possible), and a sensible wattage, should see you right, there.
Cases are a very personal thing, it's got to be something YOU like. You are the one that's going to be sat, looking at it. Corsair, Antec, Fractal are decent manufacturers, across their range. As you are not trying to cram a lot in, or overclock, most ATX mid tower cases will be ok. You just get what you pay for, in terms of build quality etc.