"Those things that" or "those things which"?
Solution 1:
In UK English it's the commas that make the difference, not "which" or "that"!
By putting the clause "which I need" between commas you are showing that this is additional information; the reader knows about the things already, but you are now telling her that you need them.
Without commas you are assuming the reader knows that you need some things, and are restricting the sentence to talking about those, and not any other things you may have mentioned to her.
In writing you shouldn't use "that" inside commas but you can use "which" or "that" otherwise.
In speech, however, there are no commas. English uses the commas because we have no way of writing intonation patterns - and that opens a much bigger can of worms for the English learner!