Will I get sick of reading and reccing River/Doctor stories? Methinks not.
Fic Title: The Ever-Growing Island
Genre: Angst, Romance
Why This Must Be Read: River's encountering of earlier Doctors isn't exactly uncommon--in fact, if you go by that "Eternity Clock" video game, it's canonical. Of course, the Doctor doesn't formally meet her until the Library, so every encounter she has with the Doctors 1-9 needs some component of deception, hiding, or selective amnesia, less time go all wibbley-wobbly. In this entry to that genre, River encounters Nine at his most self-destructive and refuses to just stand by and watch. It's a short but lovely exploration of how he's always her Doctor, even when he's not her Doctor.
Fic Title: Even if we're just dancing in the dark
Genre: Romance, family
Why This Must Be Read: River gets a good amount of flack in the fandom for the circumstances of the main event in "The Wedding of River Song." But I rather love her and her timey-wimey-spacey-wacey love affair with the Doctor, and I love this look at it in the earlier stages (for her), which takes the Doctor's long pre-River history into account and treats this pair and their marriage with honesty, respect, and a dash of hope.
Fic Title: You, me, and all that stuff we're so scared of
Genre: Angst, Romance
Why This Must Be Read: River's university years, before Area 52 and Stormcage, haven't been shown in canon (yet?) but were obviously formative in her feelings toward the Doctor between "Let's Kill Hitler" and "The Wedding of River Song." This is a particularly good look at them. DQBunny (who's an excellent author; go read everything) keeps River in perfect character--bold and intrigued by her "persistent shadow" while still reconciling her various selves. But River isn't her mother, and she's not going to be won over simply by having all of time and space as an option. Bonus points for the cameo appearances by River's flatmate, of Boeshane origins.
Fic Title: Last Words
Why This Must Be Read: River in canon is so full of life and energy that it's sometimes easy to forget that we already know where her story ends, even if we don't know how she gets there. Most fics that follow her to the Singing Towers of Darillium are bittersweet, playing on the notion that River doesn't know it's the last time she'll see her Doctor, nor what will happen to her next, whereas the Doctor knows all of that and has to both be sad and not let on the spoilers he knows. This is not that sort of fic. It will rip your heart out and make her choices in "Forest of the Dead" all the more poignant.