Only goal I can really think of is unlocking War's Retreat. Never really been a goal oriented player, although I did give Taskman a try for a few months. Surprisingly fun.
Guthixian Caches is a good minigame to pay some attention to. Anachronia also has a few useful things even early on, although most of it is for higher levels. You'll want to unlock Menaphos, since that's the low-mid level training hub and might as well get the reputation there while the content is still relevant. As longer term goals... Prifddinas and Invention are probably the most obvious ones. If you're playing ironman, there's of course plenty of other things that are useful just for them.
Storywise... World Wakes is a good one to aim for, I think. Lays a lot of groundwork for the newer stories.