Hello! I'm going to spend at least one week in Pantanal. Could you recommend me TOP places/activities there?
It's my first time in South America. I hope to see some mountains with the jungle arround and real wilderness. It would be great to have one day in a lake with clean water. I will start from Iguazu so south part will be much closer, but i can spend a day in a bus if northern part is better.

I hope to see some mountains with the jungle arround and real wilderness
Not sure you will achieve this here. The Pantanal is a wetland. It is a low lying area that floods frequently. For mountains/jungle your best bet is Ecuador/Bolivia/Peru. In Brasil, you may get that in the Amazon. But probably not in The Pantanal. You will most likely see lots of wildlife though, it is a wildlife paradise.
But I don't mean big mountains. I mean places like Bonito: There are mountains (Serra da Bodoquena) and beautiful lakes. I also saw on the map places like Serra do Amolar. I want to see both: flat wetlands and small hills in the jungle :)

Well from Iguazu you can stop in Bonito on your way to the Pantanal, but you should understand that Bonito and the Serra da Bodoquena are not the Pantanal (although they are close to it). Bonito is famous for its clear water, so spending a day or two here doing some snorkelling is a good idea - Rio da Prata is the best place for snorkelling, but is a bit expensive (currently R$132 for the tour, and approx R$50 for transport to get there). The Balneario Municipal is the cheapest place to go (entrance fee R$25), just to spend time relaxing in a river with clear water and some fish.
The Serra da Bodoquena doesn´t really have any tourist infrastructure. There is a tour you can do from Bonito which visits the Boca da Onça waterfall, which is in the Serra da Bodoquena, and the tour is a trek which takes you to see various waterfalls, including the Boca da Onça, and also gives you some pretty good views of the surroundings. However, again this is a structured tour, which doesn´t allow you to just wander off into the Serra and visit whatever you want to, and is fairly expensive (currently R$150 for the tour and about R$50 for transport).
Alternatively, the Parque Nacional da Serra da Bodoquena have their office in Bonito. They have work parties going out to the Serra several times a week. You can try to get in touch with the office, and get a lift out to the park with one of the work groups. Usually they leave at 7am and get back at about 6pm. Once in the park, I understand there are a few trails you can wander along, or you can help the group with whatever they are doing. At the moment they are working on reforesting an area of the park which was previously owned by a farmer and had been cleared to allow his cattle to graze.
For the southern Pantanal, most people who visit will do a package tour for 2 or 3 nights, staying at a pousada or fazenda based along the Estrada Parque. However, my favourite place to go is Fazenda Quatro Cantos, which is about 150km further in to the Pantanal. Unfortunately, due to logistics (it takes a full day to get there in a jeep), it can be quite expensive to visit this farm, unless you can get a group together to share the transport costs.
Activities in the Pantanal are pretty similar no matter which tour you take, and will probably include jeep safaris, boat or canoe trips, trekking, horseriding and piranha fishing.
Whats the best way of getting to the Pantanal from Rio? I thought that Bonito is the main city of the Pantanal but looking at maps now it seems Cuiaba is the so called capital city,
Can anyone offer me advice please on travelling from Rio and expenses etc, can I fly to Bonito and start from there and is it the true Pantanal onwards from there?

There are two main bases or gateway cities:
- Cuiaba (for Northern pantanal).
- Campo Grande (for Southern Pantanal).
robably
Buses are long. It took myself over to 15 hours from Sao Paulo to Campo Grande. Planes are regular and can be cheap (if you are flexible). Bonito has no airport, but cuiaba and campo grande do. If you want to go to Bonito - then head to Campo Grande.