I think -- that scorpions were the first terrestrial arthropods. I think. If that's the case, that would suggest that arachnids came before insects.
It's not a huge evolutionary stretch between scorpions and spiders, when you think about it -- if a stinger produces fibrous proteins instead of neurotoxic proteins you get spinnerets, and if the digestive enzymes produced by the mouthparts are delivered by a hypodermic method instead of "oozing" you get fangs -- a spider.
[Checks Wikipedia for fossil records]
Scorpions are believed to have gotten started around 430 million years ago. "The oldest known arachnid is the trigonotarbid Palaeotarbus jerami, from about 420 million years ago in the Silurian period, and had a triangular cephalothorax and segmented abdomen, as well as eight legs and a pair of pedipalps." <-- from the Spider article, where it says the earliest spider fossils (in amber) are 130 million years old.
The oldest insect fossil is just shy of 400 million years old.
So, it looks like arachnids (probably scorpions being among the first) got things going a few million years before insects showed up.