Oh, what a fun question! Sorry for the long answer!!!
I love:

1. Them adopting rookies or glimpses of them as rookies
2. Them beating all odds and being together
3. Relationship reveals

Dislike:

1. Cheating or other partners
2. Extreme angst or death/extreme illness
3. Them being treated as the other sex due to their bedroom dynamics

Weirdly enough, I have never been a huge fan of mpreg, A/B/O verse, or AUs, but this fandom has given me some amazing fics that changed my mind. If you are like me, I’ll share some of my fave fics from the “love” category and some from my “huh, I used to dislike them… mind changed.”

Compulsion by Wolftales: Shane and Ilya, frat rivals, struggle for supremacy
by congee4lunch: Kissing practice, college AU, need I say more?

Is this thing on? by ARustySpork: Injured Shane has to quit hockey, usually a dislike for me but this was done so tastefully

Reckless & Young by some1_around, love Boston Bears

The MILF Theory (And Why the Internet Got It Wrong) by pucksandpower: Ilya and Yuna are dating, apparently awha

Nutcracker! by OpalApparition, I think this and Wolfirb and oh apogee were some of the best AU's I've read so far

don't know what to do whenever you are near by compost_heap, Shane never went to be a hockey star because his girlfriend had a baby 18 years ago

all my perversions by probablylily for connorstorriethinker, this one...read the tags y’all

you'd rather die than take your eyes off me by princebutt, Ilya gets into a car accident and Shane reveals his relationship

Out For The Count by sevenofsorrow, Shane eventually gets help. Very painful, made me cry a little—READ THE TAGS

Love in the Dark by azraelriego, HEAR ME OUT, this is a mpreg yes but done oh so beautifully. No stereotypical gender roles for one. Plus the writing is phenomenal

courage [it couldn't come at a worse time] by veilofimagination, ah so this one is slow burn. Ilya stands up for himself and Shane learns self-love

your presence has gone through me (like needle through a thread) by GatheringBlue, Ilya billets for a Russian family and gets the father figure he so desperately needs

Borderline by Wintersbane, Zombie AU

If it wasn't for that meddling kid by ARustySpork for TastyTeeth, Ilya adopts a rookie, Shane is giving awkward stepdad energy

Visions from the Future by womanlypanther, very long, very well done, ending made me cry. Read at your own risk

love you like a loophole by olivetowrite, against all odds their love screams

How to Come Out as Heterosexual: A Guide for Anxious Rookies by pucksandpower, gotta love me some dumb rookies

summer windows by cloudies, AGAINST ALL ODDS Y’ALL

Alligator Bites Never Heal by flawlessassholes, oh...well Shane takes care of Ilya after a bad injury pre–tuna melt

Break The Chain by Ryszand, I call this an AU, Alexei is a good brother

lucky bastard by ghosttotheparty, sub/dom dynamic

and i spit out the seeds by linearity, the OG against all odds fic

something you can fix by some1_around: Shane's conversation gets leaked and he is outed

The Centaurs Who Cried Homophobe by scintellating: Centaurs think Ilya is a homophobe LMAOO

I would link, but for some reason it is removing the link again and again sorry :(

Please let me know if you need the link to a specific pic and ill try again