The only reason I suggested tiff over jpg or gif is because tiff uses a lossless compression where jpg and such are lossy. So if you edit and save, then reopen and edit and save a jpg a few times you loose a bit more data each time. Think of it as copying a tape (analog) where each edit the quility suffers slightly or a CD (digital) where it stays the same each time and the only loss was in the initial sampleing.
Fax machines use tiff is their internal file format also so its one of the olders and most widely used. There are others such, PNG is loseless IIRC.
There are also some patents and licensing issues with some of the compression used in some of the other formats which means they may not be around someday in the future if some company decided they want $ for their IP.

Anything more complex that text or tiff I have switched to open office since its just a zipped xml file which can be unzipped and modified as plain text, so even if the original program that created the file cannot be obtained you can still use the data. Microsoft Office the format is protected so you are forbidden to reverse engineer it which means in a few years if they drop support for an older version (like they did with Visio) then you won't be able to open those files.