Two good websites I like:
You must be registered to see the links
(hover over "League of Legends" next to "On the Wiki")
- Good site to check out champions, abilities, and items in detail on their own.
You must be registered to see the links
- Good site to plan out champion builds in, or just mess around and see what kind of combinations you can come up with. You can also even just use it to see what you would need on a champion for w/e (i.e., check cooldowns at 40%, see how much health from items/runes/masteries it would take to get to 3000, how much gold per second can you make max, etc.)
As far as Ahri goes, I haven't played her, but a VERY good AP item is Rabadon's Deathcap. 140 AP, and it increases your AP by 30% of your total AP. So let's say you buy it, that's 140 + (140*0.3) AP, which comes to 182 total AP. Then let's say you buy a Rylai's Crysatal Scepter. That's 182(current AP) + 80 + (80*0.3) ..... hopefully you see where I'm going with this

Another good caster item is Tears of the Goddess -build it into-> Archangel's Staff. Tears of the Goddess gives you 350 mana, 7 mana regen per 5 seconds, and every time you cast a spell (cannot be within 3 seconds of a previous spell), it will increase your max mana by 4, and it will do this until you have 1000 extra mana from doing this. Of course, the bonus is lost if you sell the item. Archangel's Staff keeps these abilities - hell, it improves upon them (it keeps the extra mana you got from using spells , so you can't abuse the two items to get 2000 extra mana). It also gives you 45 AP, and has an ability that adds 3% of your maximum Mana to your AP. The more mana you have, the better the bonus. So let's say you have 2500 mana. This ability will add 75 AP on to what you already have; and if you have Rabadon's Deathcap, that 75 becomes 97.5.
Again, like I said, I haven't played Ahri yet, but this might help:
You must be registered to see the links
Important stuff: Catalyst is a component of Rod of Ages AND Banshee's Veil, but it's passive is unique, so getting two at the same time won't boost the passive, just your mana/HP. It's okay to wait to build Archangel's Staff until towards the end, but Tears of the Goddess you MUST get early if you want as much mana out of it as possible. Grab Glacial Shroud, don't wait for Frozen Heart - it still gives a nice boost to your DEF, mana, and Cooldowns, and you can build it into a Frozen Heart later. You want boots early. Hell, I'd probably recommend tweaking this build so that you have another item that gives you movement speed, such as Lich Bane, since Ahri seems to have low Movement.