There's rarely a general answer to questions like these. It depends very heavily on your scenario. But here's an intermediate suggestion between the two choices you bring up:
Sort the list of items to be inserted (this requires sorting 10 - 30 items based on your description). Then, insert these in order. Note that once you find the position to insert the first item, the position to insert the second item must be strictly after that location (and so on, for each subsequent item), so you don't need to search starting from the beginning again. The list being inserted into only needs to be searched through in this case as it would maintain its ordering after each insertion.