I think your case choice should be dependent on lifestyle. I like the covered ones that flip open because I know I will not crack the screen if I shove it in my purse or my kids throw it in their back pack. I think the flip top helps prevent scratches too but my kids find it a nuisance and just take it off, resulting in no protection. Some of the cheaper cases are hard plastic that shatter if dropped, not worth the money. There is a plastic one that stores your ear buds in the back. Make sure you buy the protector for your generation because the buttons are not in the same place!!
In terms of screen protector, I don't think it matters what brand. Just make sure your screen is really clean before you put it on. They are relatively expensive, $14, and if put them on dirty they just peel right off. Sometimes you can find a 2 pack, but I have yet to find "bulk".