Pantanal is very a very popular tourist destination. There are also lots of suppliers to get around so it should be super easy to arrange a tour whenever you like. It does, however, get a bit pricey if you want to go by yourself. I originally planned this long ago and then it got canceled so I still had credit left over. I would probably not splurge on the high costs again if I had the choice. It does get cheaper when you are a in a bigger group so look out for that!
I actually went to the area twice in succession. I say "area" because 'Pantanal' is the entire wetland region. 'Pantanal' from UNESCO point of view (which is what you probably want seeing that you are reading it on this website) is the territory at Pantanal Matogrossense National Park which is miles away from the two nearby cities. You do technically enter going from the north but it's not really "entering". I once "entered" Los Katíos National Park in Columbia the same way by simply driving through on a boat. This is even less "entering" as you mainly drive on a lake area in the southwest corner of the park and that is after hours and hours of river cruising. But let's get through the two locations first.
The obvious one is in the north. You fly to Cuiabá and get picked up from your guides. It's the obvious way and in a few hours you will reach your lodging at the river. You tend to still do an afternoon tour on the river. This alone is glorious because you are far away from towns and birdlife, fishlife, monkeys, caiman life, fireflies all come to "life" here. It doesn't really matter if you go all the way to the national park but they do offer that long trip for the next few days. Your trip all the way down starts VERY early, includes packed lunch, and returns for sunset. You don't really want to be on the river for much longer if it's dark but you do get to see the fireflies, caimans, and...well that's about it. Caimans are better found in the dark though. Good luck finding fireflies during daylight (lame joke intended). If your main target is seeing a jaguar (and you picked the best season) it's quite likely you will see one. They tend to be at the river bank here and there and usually you see another boat watching them already anyway. You won't see them at the large lake and you are better off seeing things on the river on the way. In a way I want to say it's "better" not to enter the inscribed property but I suppose one wants to be there if so close already.
The highlight of the park is surely birding. I was very impressed with it. The rest of the animals are a bonus and surely you WANT to see a jaguar. There is a high chance to see one in the north. They tend to just sit at the side of the river. You are better off seeing them in dry season by the way but I won't get into details as I'm no expert. You can get a nice checklist of birds from Avibase (no affiliation) if that's your thing. I recommend it as you'll see birds everywhere. The below picture is the wetland bird, the Tuiuiú or Jaburu, and probably the largest you'll see around here.

I also saw pretty macaw, storks, spoonbills, and anhinga. On land there were Greater Rhea which in Portuguese they translate as ema and thus they get confused as emu. They are related but not the same animal (sorry for the bad picture quality; I took this with my phone and it was quite far away).

Having seen all these majestic animals for a few days I thought my site visit was accomplished. You even technically enter the inscribed site. But I wasn't done quite yet although I sort of wish I had. I was driven back to Cuiabá and took a flight to Campo Grande (it's daily, I think twice?) and took a transport west almost to the border with Bolivia. You don't even reach the town of Corumbá as the van will drop you off and you get a vehicle to the lodging. The road is small, dusty, and thus a 4x4 safari jeep is required. I mainly did this because I went with a Canadian buddy and he didn't want to spend $$$ bucks on safari plus he wanted to go fishing. Fishing? Well, more on that later. One spends a loonie on private lodging (aircon, shower, lots of room!) and it includes all food and activities. They also treat you really well so you can go fishing extra, a swimming pool is there too but nobody was too interested in that. So, why was it bad? Well, at first it was great. The afternoon tour on the river included many birds just like in the north. You also see caiman in the evening. You do not see jaguars much here (or, rarely, the guide have seen them but I don't think you'll expect to stay for weeks to see one). It was still quite nice though - but then the second day we went on a dry safari. It wasn't uninteresting to look at the forest but it was very hot - and you have to enter private farm land. What? As said in other reviews, private land is normal in Brazil and the government will not take away land for parks. They can try to compensate but the owners are unlikely to settle for the little money they get. One would sometimes prefer a totalitarian regime that simple takes all required land, protects it, then people don't even complain (or they don't complain due to large compensation) but I don't know the full picture to argue for/against it. Either way this doesn't exist down here and it's a bit scary. Jaguars can be killed if they enter the private land. "I make money with the cows, not on tourists seeing the jaguar".
The third day I went on a river cruise the other eastern way and it was full of fishermen. I saw them before but it wasn't as bad as that day. Every corner would be someone fishing. So my friend wanted to fish and he organized a trip just to go fishing which was definitely different than Lake Ontario and not everyone has time to travel to St. John River in New Brunswick but hey, maybe you live somewhere awesome and get to fish all the time and I'm wasting my time trying to argue. I personally don't fish but his feedback was that it wasn't as good as he expected but he certainly enjoyed his time, fished stuff he never saw before which I guess was more of the purpose. Furthermore I saw lots of ads for fishing as I was driving back so this is a big thing after all. I suppose people don't just want to see capybaras. Just for that you get the capybara pic. They tend to see you and start running away.

Finally, to sum up I highly recommend the Cuiabá north section. If you are short on cash you can choose the south section but just don't expect too much. You will only be in the Pantanal wet area and not the UNESCO inscribed property. As I said, the north gets cheaper in a bigger group so grab some folk/friends for a better deal.