TDMS files sound like a reasonable choice for that kind of data, especially at low rates, but so does sqlite.
Seems like the pros of TDMS are you can hand it off to someone and they can open it in excel, but for sqlite you need to make a reader. TDMS also is a bit more flexible about schema. While you wouldn't want to change channel counts within a file for example, you can change between files without much work. For a database you'd need to come up with a schema that makes sense for you (this doesn't mean its complicated, it probably just means you have the columns "time", "channel number" and "value"). Sqlite lets you query easily for different conditions, while for tdms you'd have to write all the logic yourself for queries. Neither of the cons is particularly bad for the situation you've described.
Your last point ( write TDMS files, then store records on which files hold what data ) is basically what diadem/datafinder do for tdms, as I understand them. So depending on your particular work environment, you may already have access to those tools which may save you some time.