What do you want to see if there's more than one sale date with the lowest price?

In any case, you can do this with a subquery and join it with the main table. I don't think there's anything non-standard about it:

  SELECT hs.*
  FROM house_sales hs
  JOIN (
      SELECT house_id, MIN(price) AS min_price
      FROM house_sales
      GROUP BY house_id
  ) min_prices
  ON hs.house_id = min_prices.house_id AND hs.price = min_prices.min_price

I'm sure you can do it with window functions as well.