I have been leaning against wood because,
1. Screen frames are usually low profile, therefore, thin. Wood frame screen will stand out.
2. You want knot free, dry and straight grain to make frames and you'll waste a lot of PT to gain the frame material you need. BTW, I've never made light weight frame of anything with PT, so I have no personal experience here.
3. Cedar is expensive and very soft.
4. You may have to add supports, etc, to existing structure to hold the screen. You may not like the end result. Some personal experiences here.
For budget screen, I think the screen repair kits are pretty good.