I currently have InDesign CS 3.0.1 and I am wanting to upgrade to a newer version. We are going to be adding InDesing on to another computer and I want to make sure that transferring documents from one of the computers to the other won't be a problem. Is the newest version of InDesign compatible with CS 3.0.1?
Your options are pretty limited. You can pay full price for a perpetual license for CS6 (and you'll need a license for each seat), or you can purchase subcriptions to Creative Cloud. The first-year discount offer for users of CS3 and later has been extended, but I don't think there is anything for user of CS (version 3.x).
In theory you can open the old files in either of the new versions (though I wouldn't -- export to .inx in CS and open that instead), but there is no way to go backward without having CS2, CS3 and CS4 as well, and you files may not be very usable after that many conversions. I'd suggest keeping CS alive as long as possible (even if it means keeping an old machine around to run it) just in case you need it, and I'd probably only convert files that will have an ongoing life.
Keep in mind that a version upgrade may also require a hardware and OS upgrade.