Maybe have a different Goko "half set" available for free every week?
I think it would be a bad idea overall to just pick a half-set. The main point of the free cards would be to give new players a taste of the game, and most newbies will benefit from starting with simpler cards to ease them in. I think that goal calls for a consistent set of curated cards (Base-only is the most natural but some others could be included) plus a very small set of cards that rotate on a weekly(?) basis.
Hmmm. Going that route, I think the cards looked at should meet two of three qualities:
1) Simple
2) Representative of its set
3) Fun/interesting
If a card is really representative, and really fun (maybe, say, Goons?) simplicity could matter a little less.
To that end, my ideas on cards to possibly include on a rotating basis:
Intrigue: Courtyard, Masquerade, Bridge, Nobles
Seaside: Caravan, Sea Hag, Lookout
Alchemy: None, I don't think this would be a good set to have any of its cards be rotated in the free to play.
Prosperity: Goons, Bank, Worker's Village
Cornucopia: Tournament, Menagerie
Hinterlands: Oasis, Border Village, Haggler
Dark Ages: Poor House, Armory, Marauder, Altar, Feodum
Guilds: Baker, Stonemason
Adventures: Magpie, Lost City, Ratcatcher, Hireling
And then maybe pick, like, 3-5 of these each week. Enough to get a taste, but not enough to overwhelm all the Base set cards.