In my experience with Chinese, there is no chicken-and-egg problem here, even though most Chinese words contain more than one character. In the beginning, you will learn many words that consist of just one character, such as 我, 很, 好, 你, 您, 也, 家, 人, 是 and 吗. You will also learn a number of words that consist of two identical characters, e.g. for family members: 爸爸, 妈妈, 哥哥, 弟弟, 姐姐, 妹妹 and 爷爷. For this category of characters, you learn the stroke order for the characters when the corresponding words are introduced.
Of course, you will also learn words that consist of several different characters, such as 先生, 医生, 学校, 中文, 语言 and 对不起. The approach is essentially the same as for the previous categories: you learn the characters and their stroke orders as soon as the words containing them are introduced. With this approach, you never learn characters "blindly", i.e. without knowing what they mean and without knowing what some of the words are in which they can be used.
In Chinese, a single character may have more than one pronunciation, but this does not happen as frequently as in Japanese, where this is a systematic occurrence. For example, the hanzi 着 can be used as
- an aspect particle for an ongoing action (toneless
- a verb, or a complement that indicates that a certain action has succeeded (
- a verb meaning "to wear" (
In this case, you learn the stroke order the first time you come across the character but you learn just the meaning that is presented in the textbook (or whatever learning materials you are using). Other meanings can then be learnt when these meanings are used in the learning materials. For example, if you first learn 着 as an aspect article and the dictionary also tells you about the character's other meanings and pronunciations, you can ignore these other meanings until you actually learn how to use them. Stuffing your brain with tidbits you can't use is inefficient.
The above approach assumes that you start learning characters (hanzi or kanji) from an early stage. However, there are a few universities that don't teach characters until students are relatively fluent, as explained in another answer.