Must be said that the most corrupt political systems include PR, indeed it may make it worse.
Italy has had various PR systems and is more than a bit corrupt, Ireland only one, but still pretty bad, and Germany's system makes ours look clean.
As for only allowing state funding, how do you allocate the money ?
It's very very easy to see that being parties voting themselves money, yet denying it to new parties. The USA is a good example.
The American example also teaches us how hard it is to ensure that only "allowed" spending happens.
The teaching unions have done various "vote for education" campaigns. We all know they mean Labour (or used to), but does that count ?
If I take it into my head to run adverts saying "Tony Blair is evil", am I supporting the Tories, or am I 80/20 supoprting them and the LibDems ?
Ken Livingstone was for a while cast out of the Labour party. If you had state funding, it would mean that he couldn't have got money. Maybe that's a good thing, but not very democratic.
What if a party is seen as "unacceptable" ?
A radical Islamic one ?
How about George Galloway ?
The EU has been trying for some time to get "undermiing" it's structure classed as illegal. What about Sinn Fein ?
Actually, it's a tricky thing to say "who" the party actally is. In many ways the Tories aren't a party, but a horde of local federated parteis who happen to agree on some things and share resources.
I'm sure you can think up good answers to those quibbles. But the deeper point is that neither you nor I will be deciding. It will be done to suit those who have the power at the time.