You've got some pretty demanding criteria there, especially if you have such wide variations in a single day.
The key is "layers" -- different pieces of clothes you can easily put on or take off as conditions change. And, for that many layers you'd probably want to have a pannier or some other sort of bike bag to carry what you're not wearing (though you could probably get by with a backpack).
Since cost is a factor, you should start with what you already have (maybe not designed for cycling) and add a few critical pieces.
First and foremost, you need some good rain clothes -- a lightweight jacket that is waterproof (or close to it) and some sort of pants that shed water well. The jacket needs to "breathe", so you don't begin to sweat too quickly. (But even if it "breathes", you'll find that it gets sweaty very rapidly.)
You also need "wind clothes", so the wind doesn't penetrate your clothing on a cold day. These should be anything that is thin but tightly woven (but not waterproof).
Otherwise, you need layers of clothes that keep you warm without making you sweat and without holding sweat (or rain) close to your skin. Wool is the old traditional favorite here, though there are many synthetic fabrics (such as CoolMax) that are better (and not as scratchy). But stay away from synthetics such as nylon, polyester, etc, except perhaps as a thin outer layer.
Cotton is to be avoided in cold weather (because it insulates poorly and holds moisture against the skin), though many of us prefer to cycle in a simple cotton tee shirt in warmer weather.
All of these clothes should fit fairly tightly, so they don't flap very much in the wind. (Though the rain jacket should maybe be a little looser than the others, both to "breathe" a little better and because you frequently need to put it on and take it off in a hurry.) Flapping slows you down and also reduces the insulating effectiveness of the clothes.
