
Exped
MegaMat Series
Car camping comfort champ, but some side sleepers find it thin.

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I’m not your size, but I do have a really hard time sleeping on the really small pads that people seem to love. Exped sleeping pads are the only thing I’ve found that I can sleep well on, and I happily carry them knowing there are lighter pads out there. For reference, I’m an athletic 5’9” 190 and my Exped SynMat is a Regular length, but “Wide” version. It takes up most of the floor space in my Nemo Dragonfly 2p.
I have an Exped as well as the bestway one often mentioned here and the zen bivvy one, and the exped is the comfiest and warmest hands down. However I can’t remember which one it is exactly (it’s an old model, now deprecated, but 7 cm deep). Also has by far the best inflation system.
If you get a Big Agnes it will squeak against the tent floor all night when you move. I use Exped. Not completely noiseless, but built differently than the Neo pads and not a Big Agnes. I have a discontinued Hyperlite, will replace it with an Ultra when it develops too many leaks just as I did the Synmat. I wish they still made the Hyperlite.
I have an Exped Synmat and it's quite comfortable. It's more "air mattress" than my Thermarest Prolite Plus but more comfortable. So much so I'm insisting my wife use my Synmat mattress instead of her existing Thermarest on our next trip. I can handle the lesser one (I hope). I think basically if you're spending some money it's always going to be more complicated than "air mattress". I think OP means a classic vinyl sack filled with air. They tend to have poor support, zero vapor management, and are cold (because air convection inside the mattress takes all your heat and moves it to the ground).
I’ve been using a similar set up for years now. Robens z mat, Exped Synmat and a Criterion sleeping bag. Haven’t had an uncomfortably cold night yet and I tend to camp in autumn and winter.
What time of year are you going? I've done a lot of camping in Iceland in a range of seasons over the course of about 7 trips, if you're going in summer you don't need anything particularly large, just think UK spring or Autumn really. I took a Synmat in May/June and it was fine. All I would say is that it's very windy and there are very few trees or vegetation so your tent needs to be able to stand up to the wind exceptionally well. I stayed at a campsite on the south cost where someone's tent literally blew away with about half their stuff in. It ended up in the sea. So get good pegs. The ground isn't very soily! Definitely take a ground sheet protector there's some spikey rocks.

Exped
MegaMat Series
Car camping comfort champ, but some side sleepers find it thin.

Exped
Ultra Series
Lightweight side-sleeper comfort, but a bit pricey and bulky.

NEMO
Tensor Series
Ultralight side-sleeper comfort, but slippery and prone to leaks.

Big Agnes
Rapide SL Insulated Sleeping Pad
Comfortable with side rails, but heavy and warmth claims disputed.

Therm-a-Rest
NeoLoft™ Sleeping Pad
Very comfortable, good service, but heavy and bulky for backpacking.

Ranked #1
Exped - MegaMat Series

Ranked #1
Exped - MegaMat Series

Ranked #1
Exped - MegaMat Series

Ranked #1
Exped - MegaMat Series

Ranked #1
Therm-a-Rest - NeoAir Xtherm Series