Pack and play recommendation?

I've only ever owned the one, so my first question, do all the mats feel like a peice of cardboard? can you get them with a bit more padding?

For context we are moving provinces, however I will be staying with family for a few months and my SO is going down first. Unless I find better arrangements, I will be in a fairly small room with my 2 month old and 2 year old. My SO is going to take the crib since hes driving. So I figured I will use a pack and play for the baby. But the one I currently own is very hard. Like I said, feels like a hard piece of cardboard haha. This ones pretty big and bulky. We plan on taking the train. Just me and the 2 kids. However, we are planning on our own cabin, and a playpen is allowed on the train. So I'm basically looking for something that has a somewhat softer mat on it, and something that is easy to pack up and carry (although my current one folds up nice I find it very awkward to carry and its feels so much heavier then other ones I've carried lol). I dont mind buying a new one especially if it's coming with us because it will get lots of use! Suggestions?