I just decided I needed to know the word for week and found both 週 and 週間 mean "week".
Can I get by as a beginner with only 週間? Or when should each one be used?
You should know both, and their differences.
Measures of time are often suffixed with -間, and in the case of a measure of time with weeks as the unit, -週間 is the preferred way to say "week" as in "an interval of X weeks".
For example:
一週間 = one week's time (or more colloquially, one week)
卒業式まであと(残り)わずか一週間です。(or 卒業式まであと一週間しかありません。)
There's only one week left until the graduation ceremony.
When speaking of a point in time that is a relative point in time, you would use just -週 as the word for "week".
For example:
来週 = next week
来週の月曜日は僕の誕生日なんです。
Next week Monday is my birthday.
So, 週 is "week" in a relative sense, while 週間 is "week" in a quantifiable sense. Neither of these words would completely serve on their own, as they usually form a part of another word that provides clearer context, but knowing what context they provide to a word helps with determining how you'll use them.
For beginners, I recommend the following:
週
when you specify a week. e.g. 第5週
= the fifth week週間
when you refer to a time span. e.g. 5週間
= five weeks.This is preferable while you may 週
instead of 週間
.