Welcome.
First, Inn is no real drawing. After you played Inn (out of a 5 card hand), you have a 4 card hand. So if you rely on large handsizes, it doesn't help you anything. Inn gives you the actions, and filters your deck, which helps to draw all the actions you can use, but you didn't have so many actions, and if you say discard a Copper and an Estate and draw a Copper and a Silver, than it's basically +2$ (you don't need the actions, and you're treasure increses by $2), which is not much for a $5-card.
Apprentice, on the other hand, is often really good. You can hopefully trash Estates for 2 cards in the beginning, other Apprentices for +5cards, Gold and Provinces for lots of cards. Especially if you can profit from this large handsizes (e.g. by +buy to buy many cards) this is really good and excelarates the game. Usually you want some "cheap" way to get cards to feed the Apprentice with. Because if you trash a say Gold for a good hand, and you just can buy a Province, somewhen soon this will stall. If you have a +buy to buy this Gold again, this will last longer. But even better here, and that's where the Apprentice gets real good:
Hoard usually already is not bad on its own. I think one can always consider to go a money-based strategy with Hoard, but large handsizes (say BM-Smithy) really help. Large handsizes lead to doubleHoard turns, where you pay $8 for a Province and two Golds. In combination with Apprentices here, the Gold then can feed the Apprentices for large handsizes, and you again gain a Province and two Golds. Also you can buy Duchies in the beginning with Hoard in play without much regret, in order to trash them later with Apprentice and keep the Gold. Additionally:
Bridges are better in masses, cards get cheaper, you can afford more of them, the Bridge gives the +buy. In the next turn, some of these once cheap cards can feed the Apprentice, to again draw large handsizes. But you need the Inns, too, and it depends a little bit on the speed of the opponent if I would also go for them or just try to quickly win with Apprentice/Hoard.
Familiar on the other hand seems like a trap against Lighthouses, especially in a deck that can be so fast that 2 Lighthouses essentially guarantee that you can't get hit by it.