Data files have nothing to do with the OS you’re running, so from that point of view you can simply transfer them from one OS to another. That said, the OS does affect which apps you can run, and those apps may not be able to open certain (older) file formats. I don’t see such issues on the horizon with the formats you list. But just in case, you may want to hang on to your old Mac long enough to test the various file types and formats on your new Mac, so that you could save possible problem files in a more amenable format at the source OS.
As to app-associated files (bookmarks, calendars etc), you can almost always export those in one way or another, and subsequently import them into contemporary apps. You might want to look at the various app menus to explore those export options, or return here with more specific questions.
In general, your plan to back up all your data files is a good one (I hope this is not the first time for such a backup!). Finally, another reason to hang on to your old Mac is that you may be able to transfer your data files via an ethernet cable or (perhaps) via FireWire disk mode. This will go faster than flipping disks, but each way should do.