There is no one food that will give your rabbits a complete natural diet year round. An appropriate selection of weeds probably comes closest and is certainly cheapest (free for the gathering) but rabbits need some grain and a good source of protein to sustain year-round breeding.
I feed my rabbits a good alfalfa/grass hay mix, a bit of grain (wheat, oats and barley are all good... I don't recommend corn) and as much fresh forage as I can manage given the season. They do well on this but growth is slower - 14-16 weeks to market weight instead of 10-12 weeks.
Everyone likes to trim feed costs, but it should not be all about cheapest. Natural feeding is a decision most of us take for a combination of reasons: the well-being and pleasure it gives the rabbits, the satisfaction of knowing what they are eating, the relative safety in the face of so many horror stories of losses to bad feed, the desire for self-sufficiency, the better flavour of the meat and, of course, the lower cost. It's a lot of work to do it right and there will be days you don't feel like gathering those weeds... so don't jump in blindly.