One for all: Leaguecraft. I practically learned play League of Legends keeping that site on my browser and playing LoL in window mode.
There tons of good guides, divided by champion. Each guide is voted by community so you can immediately distinguish between useful and garbage. And in addition every guide is linked to a patch version, so you know if they are outdated.
In addition you can check builds for League Of Legends at Moba Fire and another useful source of tips on specific champion styles and builds is of course the official forum NA or EU.
So I did some informal testing, with probably a large margin of error, I have some pictographical results.
I picked Blitzcrank, because I own him(it?) and he has a base 300 ms. 8 Seconds of walking down the bottom lane put me a little ways behind of the inhibitor.
Purchasing boots of speed boosted him up to 350 ms, and 8 seconds brought him past the inhibitor, put not yet past the inhibitor turret.
I attempted to record results for 406 and 455 (like I said, it's hard to get the higher numbers precisely) but botched the results, and in each case I was only about the same spot as 350 ms.
Finally, I bought Phantom Dancer and Boots 5, hit ghost (un-talented, sadly) and activated rank-5 overdrive to see how far I could get when speed was pushed to egregious levels. Since Overdrive lasts for 8 seconds, it made for a far more accurate timestop. I made it here.
So we can safely conclude that, unless you're backed in to your own base, it is always faster to recall.
Now if you'll excuse me, I'm going to go avenge my horrendous 6 - 4
previous test game. I will get Ashe Bot this time. grumble grumble
Best Answer
This is a very situational, and depends on your play style.
Most skilled AP Mids don't get an item based on whether it gives you more mana or mana regen. Athene's Unholy Grail (AUG) is such a good item for mana hungry AP champs such as: Ahri, Anivia, Kassadin etc. not only because AUG has amazing mana regen abilities, allowing mana hungry champs to have sustain, but it also gives Magic Resist (MR) and a decent Ability Power (AP) boost. Everything an AP mid would need to succesfully win his lane. It's also a very easy item to build up too.
Rod of Ages (ROA) is a good item because it gives mana and health and ability power. If you build this item first, Catalyst the Protector gives a decent sustain with its passive ability. Also being one of the few meta acceptable items for an AP mid to build that has health, its great for survivability
Now a days the only Champion that usually builds Archangel Staff is Karthus, and its usually 4 Archangel Staffs with Sorcerer's Shoes and Rabadon's Deathcap. This usually accomplishes the goal of being able to nearly one shot the entire enemy team with Requiem. Although I wouldn't suggest this build at all.
As a rule of thumb for my builds I usually go heavy mana regen for AP Champs such as Ahri and Kassadin. Champs that have long cooldowns, and burn through their rotation very quickly. Heavy Max Mana is great for champions like Anivia and Karthus who have very important AOE Spells that are channeled and tear through mana faster then any amount of Mana regen will keep up with.
But this is hugely dependent on play style and preference and my opinion.
If you'd like examples for more champs let me know.