The start of any new survival-crafting game always presents two great challenges - the first is always to figure out the basic shape of the tech tree. In any game of this type, you will be constantly picking up various doodads and blocks of construction materials and it is useful to know what those materials do. It also helps to know what to search for in order to bootstrap yourself up to a new tier of tools and weapons. Terraria is deceptive because its colorful and inviting 2D graphics completely belie the dizzying depth of its tech tree.
I'd say that most crafting games settle on 4-6 tiers of equipment, which tends to give a nice spread with a few intermediate stages between your initial piece of crap pickax and the ultimate landscape-dissolving pickax of ultimate power. However, with Terraria, there are 27 different varieties. Granted, some of those are variants and novelties (like the candy-cane pickax that shows up around Christmas), but even so, climbing the ladder to ultimate power is a long and arduous process. It's not something I really need to dwell upon right now, but it is worth keeping the first few steps in mind.
The other challenge is deciding upon a grand project to pursue. Something like leveling a mountain, digging to the bottom of the world, or building a totally unintentionally phallic tower of gargantuan height. The actual execution of the project is usually what marks one's transition into the mid-game, as these sorts of things usually require at least slightly upgraded tools and a ton of materials (even simple digging requires things like torches and staircases, for when your pit gets too deep), but it's worth keeping an eye out on your initial exploration, in the hopes that some aspect of the environment inspires you.
Given these two early game challenges, I think my time with Terraria has been going relatively well. I've still been cleaving fairly closely to my initial spawn location, but that is primarily because every time the sun sets, the game spawns a never-ending stream of monsters to attack my humble wooden shack. Frankly, I think it borders on the excessive. If you're anywhere near the surface after nightfall, you pretty much have to devote all of your attention to fighting off monsters. Either that or huddle in a shelter all night. It's like a waste of half your time.
Of course, there are ways to deal with this, and this is exactly the sort of early-game problem that spurs you on to advance your character's power. It can be a bit uncomfortable at times, but I have to concede that it's a stage that makes the game stronger overall. Later, when I'm fighting fire demons in the pits of hell, I'm going to remember the time when I was threatened by zombies and slimes and it's going to bring me comfort, because I'll know that the only reason I have end-game problems is because I succeeded at solving all the problems that came before.