Yes, and unicorns can roam the fields. Are you really that naive?
Funded by the people heh? So who all gets funding, everyone? You have to set thresholds... and without any money, who's going to be able to meet those thresholds, and how?
If you try and take personal money out of the equation, first of all you're going to be at odds with the constitution. Second, you're never going to be able to take it out anyway, because someone can always use money to pay people to hand out flyers, or go door to door to do stuff etc, you're not going to be able to control that without shredding the constitution.
I also agree with DT, if you were to magically take all the money out of the process (when pigs fly), the media would essentially control politics. It would be free to cast each candidate in the light it desires to get the desired outcome. For example, they can treat candidate A (who they don't like) like dirt, show bad pictures of them, run negative "news" stories on them, while candidate B is portrayed as the savior. No thanks, we already got a nice little taste of that in 2008.