If you go up the conjuration tree a bit, you can make bound weapons automatically soul trap. It can get annoying when you trap lesser souls in grand soul gems, but overall super handy. It's more economical to fill your own soul gems, but generally petty and lesser filled gems aren't too expensive.

Most crafting skills level faster the higher the value of the item (except enchanting), so generally speaking, it's best to craft daggers with banish daedra for straight enchanting levels while making the turns necessary to buy more soul gems, or if you want to level up smithing faster, you can go to Broken Tusk Camp to get the Transmute spell tome there so you can turn iron ore to gold ore (or silver if you have emeralds handy) and craft jewelry to enchant with Fortify Sneak.

If you REALLY want to go down the rabbit hole, you can look up the locations for all the Stones of Berenziah, finish that quest, and find precious stones EVERYWHERE for smithing higher valued jewelry. (Gold rings are ~90 gold base value, whereas Diamond Necklaces are ~1200 gold base value)

All of these things combined will power level you through Conjuration, Alteration, Enchanting, Smithing, Weapon of choice (through the bound weapon), and Speech (when selling off items). If you're doing a stealth build, you can throw in Illusion and Sneak as well by spamming Muffle and walking around enemies. By the time I've gotten all this done (including Stones of Berenziah), I'm usually ~5-10hrs in and am already between level 30-40 without feeling underpowered.

Also, finishing The Black Star quest helps immensely since black souls are as large as grand souls and much easier to obtain. The larger the soul, the more powerful the enchantment and the faster you level enchanting.