What you craft really depends on what you have access to. Thus, it depends on where you are in the game and what resources you have. The more valuable the item crafted, the more skill points you receive. Thus, there are many factors. One is how much time you want to spend leveling the Smithing skill. Another is how much money you have.
If you want to "live off the land" so to speak, then crafting leather items from hides you hunt is a pretty good deal. As you mention, animals are plentiful. However, from a time-to-skill-experience perspective, it's not that great. Hunting takes a lot of time. But hey, maybe that's fun time for you, so that's fine.
I make a lot of money off of potions, so money's not really a problem. I think I can count the number of times I mined for iron or hunted for hides on one hand.
When trying to powerlevel my Smithing skill, I tend to throw money at the problem. Thus, I will travel between holds and buy all of the shopkeeper's inventory I can afford that could be used for crafting. I then lumber my overencumbered character over to the smithing tools and then craft the most expensive things I can as fast as possible. Then I sell the results at a profit. I can then fast travel to another shopkeeper and buy up all their stuff and repeat the process.
When doing this, it used to be the Iron Daggers were the way to go. I'd still probably recommend them if Iron and Leather are the most you can afford or the best you can do. At 1 strip and 1 iron bar, a single Iron Dagger is relatively easy to craft.
If you have more Leather than Iron, you can make Leather armor as well. It's a very good armor to craft for selling for profit. It just takes more Leather, which the shopkeep might not have lying around this particular day. Usually after buying but before crafting, I'll come up with a plan as to how much Leather I'm going to make into strips, and what I can make from the resulting materials. Thus, at low levels at least, I'll make plenty of both Leather and Iron gear.
Different items crafted from the same materials have different values - the ratios are not constant. Thus, it pays to know how much it costs to make something versus how much you can sell it for. You will find that there are better and worse ways to invest your raw materials - some things (like almost all the Hide armor bits) cost more than they're worth!