I'm coming up on beating Unova, and once that's done I'll have all 5 main stories done and dusted.  I can finally start prepping for post-game stuff and the more "MMOish" side of the game. What sort of things should I get up to?

You have the legendary birds & beats to catch with the birds in Kanto and the Beasts in Johto. They are rotated every 1st day of the month so you have a while to hunt them both however the encounter rate is 1/9000 but this number isn't confirmed by the devs. they are roaming so there isn't any static location to find them so you'll have to search in the grass/water but take note, they cannot be found in caves. Places you can fly from, you can find them. For example Veridian Forest you can find them in there.

--Kanto Birds--

Moltres - Grass/Water
Zapdos - Grass/Water
Articuno - Grass/Water

--Johto Beasts--

Entei - Grass
Raikou - Grass
Suicune - Grass/Water

Once you beat all the regions you are considered to be mid-game. I'd recommend getting a Adamant 31 Atk, 31 Sp Cloyster with the ability skill link to start doing trainer re-runs with to build yen. After that i'd recommend getting a Gym re-run team with x2 31 Sp.Atk, 31 Speed Typhlosion's with a Archeops with 31 Sp and has Tailwind. You'll need a Blastiose with the egg move Spout which also runs 31 Sp.Atk, 31 Sp. Next is Torkoal with the ability drought to increase fire move damage.

You'll need x2 Choice Specs to give the two Typhlosion's to boost Eruption Damage. 1 Choice Specs to give to Blastoise to increase Spout Damage. Last two are one Heat Rock for Torkoal which increases drought to 8 turns and Wide Lens for Archeops to make Rock Slide have 100% accuracy.

Lot of information to take in but i'd start with trainer re-runs till you can afford the gym re-run team.

Its all about filling that Dex so you can go to Mt.Silver and battle Red!