The Hall of Monuments itself, which you require access to in order to dedicate armors+minipets+etc is located in the Eye of the North expansion so that's an essential acquisition if you're seeking HoM rewards. You don't need it immediately though - it's fine to obtain the in-game things now and buy EotN later if you can't do so now.
As for points, it's theoretically possible to obtain 43 of the total 50 points with only Prophecies and EotN so that's not a concern. If you're only seeking 10, your best bet would probably be (assuming you get EotN):
Honor: Accounts Linked (3 points)
Honor: Any statue (complete Prophecies for the Hero of Tyria statue - 2 points)
Devotion: Any miniature (1 point)
Fellowship: Any hero statue (1 point)
Fellowship: Five companion statues (2 points)
Fellowship: Any pet statue (1 point)
There are plenty of others which are within reach for a new player. Different ones require different ratios of time and money. See here.