Might as well ask "how long is a piece of string?"
There are "typical" sequences of archwires that might be used, but it's by no means a "one size fits all" scenario. For example, some (particularly malposed) cases might require an especially flexible initial archwire, in which case they might begin with a coaxial wire, rather than the usual .014" or .016" round NiTi wires - here's a pic I found:
Or, as another example, the orthodontist might want to open up a deep bite, and might therefore choose a reverse curve archwire:
But, if you want to know what a "typical" sequence might look like, see this article
(Scroll down to page 6) which discusses some recommended archwire sequencing with the SmartClips bracket system.
I should add though, that even if your ortho doesn't use the sequence outlined in that article, it doesn't mean that (s)he is doing anything wrong!
Btw - here are some illustrations of archwire types: