There are a great many of items on the Fields of Justice, but not all of them are incredibly powerful, although these undermined items often have much smaller price tags. How often should someone use items like Haunting Guise and Doran's items, which all have important stat combinations that aren't often seen elsewhere. Is it better for me to focus on getting items I can complete early on, or save up for something larger like Infinity Edge or Rabadon's Deathcap?
That depends on each match you're playing.
If you can always save up for the best items,however if you're having problems farming creeps and things like that because enemies are stronger then you and they're giving you too much trouble then buy few more doran items or something else that is cheap but gives nice decent stats for the price (like wriggle for AD champions because it's very cheap and gives pretty good stats). Of course once you fill your inventory sell the weak/cheap items you bought before to make you more viable in game and buy something better.
It's all situational. Does your champion scale better in late, mid, or early game? I'd say this question particularly deals with ap and ad carries because of doran's ring and blade. There are different builds to each hero, and it all depends on how you play them. For instance, 3 doran's rings early game is a great move on Leblanc and Cassiopeia it gives that extra mana regen and ap that they need to secure a successful early and mid name.
The kills, easier last hits, and sustain you get from these dead end items tend to be worth the cost in most cases.