Brenan,
If I were you, I'd use a 2x4 framing kit like this..
http://www.amazon.com/Fast-Framer-Universal-Framing-Kit/dp/B0000AXFST
Saves a lot of time and very inexpensive

Tom

Brenan,
You can get a book on framing, including post and beam framing, that can guide you through this process.

Personally, I would just use 8 foot 4x4's at the corners as my corner posts, then I would use 2x4's as my bottom and doubled top plates. I would also use 2x4's spaced every two feet between the posts to give more support to the top plate, and to give you a place for nailing the purlins to attach your screenwire to. The purlins can be 1's spaced about every two feet from the top to the bottom plate. You will also want to use 1's to make a diagonal brace running from the top plate to the bottom plate at the corners, and nailed to the studs in between. As far as rafters you can use either 2x4's or 2x6's if you stay under twelve feet between the top plates, and keep your spacing down to two feet. You will also want to diagonally brace from corner to corner, from side to end top plate under the rafters. The bracing will prevent any problems with your screen house from racking out of square. You will want to nail furring strips over the top, bottom, corners, and where ever else your rolls of screen wire meets. As for the top, I would suggest you look at polycarbonate roofing panels instead of canvas or a tarp. The fabric will eventually sag, and be more susceptible to damage, not to mention holding water.

As to the connectors, most of them are galvanized steel and meant for exposed as well as hidden uses. I would use either coated deck screws or coated/galvanized nails (sinkers) that are at least 10 or 12 penny in size. If you go with the roofing panels you will need to use either nails or screws that are designed for this use. They have a washer under the head to prevent leaks, and the shank is grooved spirally to prevent pull outs.

I hope this gives you an idea of what you will need to do.

Kevin