Best couple?

Firestar x Sandstorm is most likely one, along with Cloudtail x Brightheart throughout the series as a whole. Out of my own bias and in my personal opinion, I'd say the best are those two and Jagged Peak x Holly; Berrynose x Poppyfrost; and Mousewhisker x Hollyleaf. But those last three are just me and my big fat bias speaking.

Ferncloud and Dustpelt, the second was destroyed after Ferncloud death and the part that he says that he keeps the old most of her bedding strikes my feels for super effective damage.

Heathertail and Breezepelt, it began as a crush that Breezepaw had in the first book of PoT and goes all the way down to CT, he getting shy after she praises him was like the cutest thing and not really common in the warrior universe.

Lionblaze x Tree, no, not the cat but the plant, in his head preferably.

Firestar x Sandstorm's the best of the best motherfricker. :U
They're healthy and they communicate with eachother, their personalities compliment eachother perfectly with Sandstorm being Firestar's rock and him needing someone feisty, and Sandstorm needing someone gentle for her. They're are wholly devoted to one another despite their ups and downs, and had a good slow-burn build up to their relationship for a good 4-5 books i.e 2-3 years in universe to get close, despite them not being too fond of eachother at the start.
Even when they were both demoted to BG characters you could tell they loved each other dearly, and even had some cute moments then. (That bit in Jayfeather's PoV early in Fading Echoes, I think it was, about Firestar dreaming of him and Sandstorm's night hunting antics that they do when everyone else is asleep gets my heart EVERY. FRICKING. TIME. They have the BEST marriage, they have no RIGHT to be that cute.)

Also some really good ones:
Dustpelt x Ferncloud - A healthy BG couple that was super sweet and Fern complimented Dust really well with her softening him up. He was devastated at her death too, it hurt seeing him grieve for Ferncloud by wanting to keep her bedding to have her scent still be there.
Brackenfur x Sorreltail - Simply put, a drama-free couple that's also healthy and cute. I hate that Vicky ruined them for of the fact that Sorrel was "too happy" and they were "boring" to her because they had no drama. Ugh! _{(Wish I can re-find the source for that because it took a LOT of digging to find to begin with and was a long time ago)}
Cloudtail x Brightheart - Cloudtail helping Brightheart with her insecurity about her injury and even helping her be a Warrior was touching. They're both alive and still going strong too, which I'm surprised by tbh.
Crookedstar x Willowbreeze - They had build up and were so devoted to eachother it's cute as frick. Willowbreeze loved Crookedjaw and his disability didn't hinder that. There was no "I love you... and your jaw." implied with her. No, it was "I love you and all of you". Also, they had tickle fights... TICKLE FIGHTS! Hello???
Breezepelt x Heathertail - They had history, are seen together quite a lot, they had build-up and Breeze values her as a friend, and Heathertail was there defending him when he needed someone there for him, especially in CT when he got a lot of hostility from his own clanmates. Breezepelt being astonished Heathertail even WANTED to be with him, along with how you can feel his happiness when talking about her such a way was so sweet and they were such a wonderful pair and I'm glad CT gave them the development they deserved, and they too are healthy as a couple!

sorrel / bracken
jagged peak / holly
tall / jake
I like crooked / willow but it kills me

If only we read the same books of the first arc where she shows to stop being so rude towards Fireheart after the second book and warms up to him and soon grows an actual genuine bond with him. Oh wait... :U

Also her being so stubborn to hide her pain is pretty IC for her if you want my honest opinion (Being stubborn and fiery is her thing so I'm glad that didn't go away).

Adding onto this, the only reason Sandpaw didn't like Fireheart at first was because she thought he was a weak kittypet pretending to be a warrior. Once he saved her—thus seeing his bravery with her own eyes rather than word of mouth—her outlook changed. It didn't really come out of nowhere. The next time they interact, she's all awkward around him and even after they become friends and later mates, they still have issues to work through and they eventually do.

As for not trusting him as Firestar, is this referring to him and Spottedleaf? Because to be fair, she had every right to be suspicious. Unlike some other jealous cats, Spottedleaf actually did like Firestar and vice versa this seemed to be well known. Sandstorm is also a very insecure cat, and finding out that her mate's first love was visiting him in his dreams without her knowing... Of course she was going to get upset over this!

Also, I wouldn't call what Sandstorm did in her final moments stubbornness; if anything she seemed to be trying to put off her own pain for her grandson's sake.

Obviously Fire x Sand, then Tawny x Rowan, and Leaf x Crow. Yes, I know the last ones unpopular but I love it.

My top three favorites are FernDust, CloudBright, and FernIvy :') When someone asks for my favorites, those are the ones that immediately come to mind!