We actually already got 1 and 2 in paperback, whereupon publication ceased, so I'd suggest starting with 3. There are 9 total.
It qualifies as "Light novels where an adaptation is available in English (e.g. anime)"
See https://dirtypair.fandom.com/wiki/Dirty_Pair_(novel_series) (which doesn't mention #9, which is recent).
Publisher: Hayakawa Publishing
I have a certain sentimental fondness for this series; it was one of the very first that I saw scattered episodes of back in early 1988 when I was first introduced to anime, while in grad school.
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@arromdee I would love to read these.