If you need to go through multiple walls, you probably need more than one access point. That's my rule of thumb.

At my last place, I positioned the main router at the end of a hallway. I could hold a signal all the way down that hallway, but as soon as I turned the corner the signal died. Any other positioning just meant it was going through more walls, so it only made matters worse. So I set up an additional access point, connected via a long-ass ethernet cable strung along the ceiling. Just like that, perfect coverage in all rooms.

You should definitely experiment with router position and map the signal strength around different rooms before shelling out money. You want it to be as simple as possible while meeting your needs.