I'm always surprised by how few people really learn to master GMail especially as more businesses use it and grumble because it's not Outlook. I find I'm more productive in Gmail than most of the well-known desktop email, but there are a few things to learn.
In other email programmes, they're folders, but GMail uses labels. The same message can have multiple labels so you can boost your chances of finding things later. When you 'Move to…' you're really labelling and archiving.
When you've got the kind of job where you will have to refer back to emails, taking the time to set up a few sane labels can make a huge difference when you're searching later on.
Gmail already does a pretty good job of showing you the result you want with a plain search. But when you're looking for that one email among hundreds, narrowing it down can save your bacon.