First, how wide a tire?

Secondly, why a rear brake?

I've never had a rear brake on a fixed bike, partly because I have my legs to do the amount of braking one can expect from a rear brake, and, more importantly, it seems (I don't know 'cause I've never done it) like an unnecessary complication to adjust the rear brake for a different cog or chainwheel.

Thirdly, why a flip-flop hub?
I had a flip-flop hub on my Pista when I got it, and found it more trouble to flip it just for a gear change than the situation warranted.
As for a flip-flop hub giving one a backup in case of stripped threads, I use only one brand of cog (EAI only) and I think that gives me considerable protection from stripped threads.
The flip-flop thing doesn't matter, though, because I think all of the budget bikes (San Jose?) come with a flip-flop hub.

For most of the year I ride with an SKS race blade fender in back; nothing in front.
When it gets really icy and rutted, I switch to my geared ice bike with mega-studded tires and big steel fenders on both ends.