winning the republican primary would probably take more money than winning the democratic, but republicans have more money. once candidates have won the support of their constituency, they should be on an equal footing financially.
public funding would be predicated on numbers of supporters. if you pass a certain threshold, you get it. it might work to have tiers of funding to facilitate the participation of smaller parties. the top two parties in terms of popular support get $20 million, for example, and the next two get $5 million, and the next two, $1 million.