How much vegetables you give them really is a personal choice. Some choose not to give them at all and others give only a small amount while others a larger amount. I personally think they should be provided to rabbits and i give a good amount to my four rabbits. Mine would have about two handfuls of leafy greens each.
You can spread it out and split up the portions so its some on the morning and some at night. This is actually better for them as rabbits are grazers so its best to have small meals at different times rather than one huge meal. I used to give morning and evening but currently I just give them a piece of pepper every morning when I am giving it to my guinea pigs. But I will be going back to feeding a small amount every morning and then a medium amount every night.
Mine get cucumber and cabbage regulary.
Any lettuce can be fed except for iceberg lettuce, herbs are great for rabbits and I find they are a huge favourite but not chives so things like parsely, corrriander, basil, mint.
Cabbage, brocoli, brussel sprouts, pok choi, can sometimes lead to gas but I feed all that regulary and never had any problem, carrots should be kept to as a treat but carrot tops are a favourite.
Celery is fine but should be chopped up in to 1/4inch pieces to prevent chocking on strings, rocket and kale are fine, tomatos are fine but dont over do them, spinich is ok on small portions but not to much and not to often,
Also fruits can be fed but should be a treat. Fruits like apples, pears, watermelon, oranges, banana, blueberries, strawberries etc.
You can also pick things from outside like dandelions, plantain,
brambles, etc.
Basically when feeding vegetables you want to focus on leafy green vegetables. Introduce one at a time and slowly and i your rabbit turns his nose up at it then introduce it again and again in a few weeks time as they may start to like it.