Took the info from multiple online spreadsheets of card and deck lists. Here is a breakdown of card rarity and card types per deck and house.
Rares: Between 2-7 rares per deck with an average of 3.24. Currently the max for a single house is 4 rares with each house having a 78.3% chance to contain at least one rare.
Uncommons: Between 3-15 Uncommons per deck with an average of 8.48. Currently the max for a single house is 6 uncommons with each house having a 96.4% chance to contain at least one uncommon.
Commons: Between 18-30 Commons per deck with an average of 24.22. Currently each house contains at least 3 Commons but no single house has been a full 12 commons.
Actions: Between 7-20 Actions with an average of 13.28. 1-11 Actions per house with a mode of 5 Actions in every house.
Artifacts: Between 0-8 Artifacts per deck with an average of 3.46. Each house has a 68.1% chance to contain an at least one Artifact.
Creatures: Between 10-25 Creatures per deck with an average of 17.48. 1-11 Creatures per house with a mode of 6 Creatures in every house.
Upgrades: Between 0-5 Upgrades per deck with an average of 1.78. Each house has a 46.4% chance to contain an at least one Upgrade.
Based on this info, it seems as if every single house is guaranteed to contain 1 Action, 1 Creature, and 1 non-Common. I don't know how much more we can deduce from it - maybe a minimum of 2 rares and 3 uncommons per deck?