Yo,
I don't know what "perspex" is but I've had the oppurtunity to try plastic, plexiglass that is. It's cheap and easy to work with but it doesn't like to stay flat. It sags. It also has different properties than glass as to what wavelength light it allows in. I don't think it is recommended as good for a planted tank.
I think BD-B is right. Glass is your best bet. If you were going to use use wood I guess you could create a glass window to allow for a strip light?
Don't know who sells custom lids on-line, but any aquarium retailer sells glass covers for standard sized aquariums.
Good luck with whatever you try.
pdid