Here's the cheat sheet on the commands:
hg update changes your working copy parent revision and also changes the file content to match this new parent revision. This means that new commits will carry on from the revision you update to.
hg revert changes the file content only and leaves the working copy parent revision alone. You typically use hg revert when you decide that you don't want to keep the uncommited changes you've made to a file in your working copy.
hg branch starts a new named branch. Think of a named branch as a label you assign to the changesets. So if you do hg branch red, then the following changesets will be marked as belonging on the "red" branch. This can be a nice way to organize changesets, especially when different people work on different branches and you later want to see where a changeset originated from. But you don't want to use it in your situation.
If you use hg update --rev 38, then changesets 39–45 will be left as a dead end — a dangling head as we call it. You'll get a warning when you push since you will be creating "multiple heads" in the repository you push to. The warning is there since it's kind of impolite to leave such heads around since they suggest that someone needs to do a merge. But in your case you can just go ahead and hg push --force since you really do want to leave it hanging.
If you have not yet pushed revision 39-45 somewhere else, then you can keep them private. It's very simple: with hg clone --rev 38 foo foo-38 you will get a new local clone that only contains up to revision 38. You can continue working in foo-38 and push the new (good) changesets you create. You'll still have the old (bad) revisions in your foo clone. (You are free to rename the clones however you want, e.g., foo to foo-bad and foo-38 to foo.)
Finally, you can also use hg revert --all --rev 38 and then commit. This will create a revision 46 which looks identical to revision 38. You'll then continue working from revision 46. This wont create a fork in the history in the same explicit way as hg update did, but on the other hand you wont get complains about having multiple heads. I would use hg revert if I were collaborating with others who have already made their own work based on revision 45. Otherwise, hg update is more explicit.