I would go with a patio cover with real roofing of some kind. The lattice is useless. It won’t provide cover from the sun or shelter for your outdoor furniture,
Depends on how fancy you want it and if you want to get a permit. Do you already have anchors for the posts? I’d say $2,000 and up. You may not be able to build it you have a small lot with setback requirements (check with the city).
