Questions about ground planter boxes (grass, tomatoes, vegetables, front yard)

[Fields of Green]

I'm going to build a planter box or two, probably 4' x 8'. Its so wet here I thought I'd build it with Trex or similar plastic board material and don't plan to put a bottom on it, because isn't the idea to let the plants root into the ground below? I was going to put some type of small chicken wire on ground under it to keep gophers/moles from moving right in. The boxes are going to be on top of grass, so what product do you recommend to put on the ground to kill the grass/keep it from coming through? Weed cloth? Sheets of heavy paper (I used this for my front yard rock perimeter planter "box")? Again, I'm thinking I'd want the plants to root into the ground over time, does weed cloth prevent this? Or do vegetables not root that deeply anyway/would I be removing the plants (tomatoes, broccoli, spinach, squash, maybe a melon) at the end of the season anyway?

How do you guys do it?

Thanks for any advice.

[Bulldogdad]

How deep will they be?. All the dirt will smoother the grass if the planter is deep enough.

[mamh]

Take a look at the Square Foot web site and how the boxes are build.This will easily show you and answer your questions..
good luck