Here is my 1984 Norco that I converted into a fixed last year.
Just under 20lbs - a great bike for commuting or exercise.
The whole "project" cost me under 200$, although I got really lucky with the frame. I would need a bigger chainring now since the bike has helped me get in shape and now I find it too easy to ride
I only bought 2 tools so far: crank puller and a chain tool, the rest of the tools are pretty common (15mm, allen keys of different sizes, etc).
Also, do a google search. There are community bike shops in Montreal; they have tools and they will help you/teach you to fix your bike. It's often free or for a small donation (like 5$). UdeM, McGill and Mec come to mind...
I tried my friends' fixies and I simply couldn't go back to "normal" bike, I really like the fact of constant pedaling! You feel more attached to the bike, you have a lot more control over the bike. The bike is light, fast and really fun!
If you are out of shape, going up the hills might be hard at first but it gets easier every day. If you think about it, people just got lazy.
Back in the day bikes didn't have gears. All bikes had ONE single speed and imagine that - NO ONE DIED! People were in better shape - a fixie will help you get there.
As someone already suggested,
Sheldon Brown is a great resource.
A few more things:
1. Make sure you select a frame that fits you well. Very well. Very very well.
2. If buying a used bike as a donor, ride it with no handlebars. If the bike pulls to either side - the form is probably bent, stay away from a bike like this.
3. Make sure the chain is tight.
4. You might want to start with a smaller chainring then upgrade later.
5. Use proper tools - it will save you time and broken bike parts.
6. Leave the front brake on the bike.
7. Get straps, especially if you are going brakeless.
8. Wear a helmet. Yes I know they are ugly. Yes they do save lives.
9. If someone wants to steal your bike - they will, however a 50$ lock will discourage most amateur thieves.
10. Get a MEC membership.
11. Have fun