I found this video to useful when it comes to deciding what to eat and what not to eat:
Lycopene is fat soluble apparently so unless it is consumed with fat you won't absorb it.
I am a bit of a foodie and I was veggie for 30 years (did me no good whatsoever re not getting cancer in fact the dairy part of it was probably bad news)
Anyway I basically follow what the doc in the video recomends: So grass fed animal products where possible - the only way you really garuantee that is organic.
Loads of green leaves, lots of tomatoes, olive oil, rapeseed oil, linseed, fish, nuts
reduce / avoid carbs (inc potatoes / bread / rice) if you can't avoid always pick wholemeal, dairy, and anything with omega 6 in abundance eg sunflower oil.
Don't eat any sugar if I can help it - chocolate is a problem here!
Note I don't actually exclude anything so I still enjoy the odd steak, pizza and I always have capucino because frankly this life is for living!!
So to sum up vegan would probably be a good option but I have no idea how you have an enjoyable vegan diet without carbs! Oh and Vegan is not sustainable without serious nitrogen inputs and without animals that can only come from oil so is unsustainable.