I would propose using the program "tor". It has already a network of thousands of servers, it is free, it is reliable (if one some server fails, it automatically routes traffic to a different one; individual connections sometimes die, but the whole network is never offline --- you can press reload and the connection goes through a different server) and it is anonymous (the traffic is routed encrypted between 3 servers before it reaches the destination).
It transfers cookies fine and doesn't modify html. As for data changing --- it very rarely happens due to buggy servers, but it is not common, you can normally browse with it. It is slow, about 10kB/s.
The downside is that some websites block tor servers. If you will abuse the website (flood discussion board, create too many accounts...), the administrator will probably after some time realize what's going on. Due to anonymous tor architecture, the administrator won't be able to find out who is abusing his website, but he can know that it came from tor network and ban all tor servers. If you won't do abusive behavior, you can live with tor pretty fine. I use it too.
You can download tor for free from Internet (and configure it) or if you want me to configure it, modify it according to your needs (for fast server changing) and make an easy to use installer, accept my bid.