I've learned that 的 can be used to say that some noun has some quality, for instance 你说的太快了 is saying that 你说 (your speech) has the quality of being 太快了 (too fast) or in other words "You speak too fast". I'm now learning about the word 最 which is defined as "the most; -est; (indicator for superlative)" and the example they give is 我要最便宜的手机。In this sentence they're saying they want the cheapest phone but the order of the noun and adjective have switched places. Wouldn't the correct word order be 我要手机的最便宜 in order to say that you want the cell phone with the quality of being the cheapest? Or does the order not matter?
There's a couple things getting mixed up here.
Firstly, 你说的太快了 shouldn't use 的 but rather 得 so it would be written:
(Although it seems that most people online cannot write this correctly either.)
Verbs can only be qualified by: 得.
的 can modify verbs into nouns.
说的 - the things said
画的 - the thing drawn (i.e.: the picture)
写的 - the thing written
This is why 的 is wrong in the example you give because 说的 refers to the content of what was said and not how it was spoken.
我要手机的最便宜 is basically nonsensical and almost equates to something like:
- I want phone's most cheap
whatever that means.
Most Chinese sentences are SVO (subject + verb + object) and here the A (attributive) modifies the object so it becomes SVAO.
Written Chinese has a page talking about attributives with the 的 particle:
Between the attributive and the subject and object, is the ‘的’ particle. 的 is the mark of an attributive, although the ‘的’ particle is not used for some attributives.
Examples of attributives with the 的 particle
（美好）的时光总是过得很快。 ( (měi hǎo) de shí guāng zǒng shì guò de hěn kuài.) Good times always go by quickly. (Time flies when you’re having fun)
（桌子上）的花开了。( (zhuō zi shàng) de huā kāi le) The flowers on the table blossomed.
An example of attributives (without 的)
他喜欢上了（那个）（红头发）女孩。(tā xǐ huan shàng le (nèi gè) (hóng tóu fa) nǚ hái.) He is falling in love with that red haired girl.