Fixies are cheap as there is not a lot on them, no gears/controls, mechs etc.
The Bianchi Pista are nice bikes but the ones I've seen are sold as a true "Pista" i.e. track bike. This means that the fronk fork is not drilled for a brake and wouldn't accept one, so you would have to replace the fork with one that would. (You only need a front brake as your legs are the rear brake).
I like the Pearson's and they are both well built and well equiped (with the bonus of Pearson's service). The Langsters are nice bikes but are not as well spec'ed (sp?). I'm not sure you could fit full 'guards should you wish (or a rack), don't know if either of these would be a concern. The Pearson has a carbon front fork and slightly more relaxed angles so is designed as a comfortable bike to put some miles in.
Depends on how much you want to spend and what use you'd get. The Langster would make a good bike and the lower spec bits wouldn't break straight away so you'd get enough miles in first. Then you could upgrade them later in the day which would spread the cost.
For a true budget build the ebay, old steel frames route is a good one. You also have the advantage of true retro class. Building up yourself isn't a problem.
-Bottom bracket and chainset - Shop could do this if you can't and would be cheap.
- Front brake
- Chain
- Wheels
- Handlebars
That's it, you can't really go wrong.