project Peugeot (help me!)

I'd point you toward sheldonbrown.com. He likes fixes and french bikes, of which your peugeot is one. His site can be like the labyrinth though.
I made a SS out of one of these same bikes bout 6 months ago. Watch out especially for the french thread bb; you might have to spend 35 bucks and get a new set of thicker cups for it in order to run a taper spindle (as opposed to your cottered one). I the whole rig to my friend for the cost of the new parts I used.
Do as much swapping of parts as you feel is necessary, but I'd caution you against going overboard on new parts as well. Peugeot px10's were nice, but this isn't a px10. You'll probably want something nicer eventually.

bikeforums.net singlespeed/fixgear forum. check there- don't add 500 tags that don't relate to your bike that is just plain annoying.

the Peug is a great start, but It's not really worth spending money on in the long run. I'd say don't change as much you can. It's your first fix, just learn how to ride it. leave the brakes ON because you'll probably need them until you get the right muscle groups. look for a cheap 700c wheelset, get a cog, lockring and MAYBE a comfortable saddle. I'd probably leave it alone after that. see you around town.

Hey there, you've got a sweet bike to work with there, a ton of potential. If you have any questions on what your doing just send me a message.

First rule when it comes to fixies is no brakes and no shifters. You can also get rid of the derailer, the cassest(its the 5 gears in the back).

Also, if I where you, I'd go to the bike shop and pick up a new single speed crank, it will be a lot lighter than your existing one.

Lastly, depending on where you live, a 16 tooth cog(the fixed gear in the back) and 42 tooth crank is the best set up for a moderately flat city.

Cheers and goodluck