I've seen take it, take that, get and catch? Are all valid or are there other ways?
These are all valid.
На is a particle you sometimes use in speech when "giving" something to a person, verbally encouraging them to "take, get" it. Often used in the beginning of a sentence, or as a one-word sentence. Its plural/polite form is "нате", though, strictly speaking, their usage differs a bit.
This "take it" meaning gives rise to a few metaphorical uses in set expressions. In such expressions на and нате are not, as a rule, interchangeable.