The lack of Item room isn't as well compensated by the starting items when compared to the other challenges. Isaac also doesn't start with an active item.
Shops can sell Mom's Purse, allowing a second trinket or Smelter allowing the tick to be smelted and new trinkets to be picked up.
Shops can also sell Hive Mind, which will make blue flies and blue spiders bigger and stronger.
Isaac starts with one item each for the Spider Baby transformation and the Beelzebub transformation, meaning only two more items from each set will grant Isaac special abilities. While the lack of treasure rooms somewhat limits the possibility of completing either transformation, it is still possible:
Hive Mind counts for both transformations ( just the Beelzebub transformation), and is in the Shop pool.
The only other shop item that's in the Spider Baby set is Spider Mod.