12.04 is a LTS which means it is provided security updates for five years without needing to upgrade to a newer release. Note that these updates do not upgrade everything to the latest version and non-security updates are only pushed back to fix major bugs.

The .1 on the end of 12.04.1 indicates the LTS has been re-released bundling in a load of updates. This means you'll have fewer things to upgrade after you do an install.

12.10 (a non LTS release) will get similar upgrades but for just two years. If you went with 12.10 it would probably be expected that you upgrade to 13.04 after its release but that isn't necessary until you want (as long as you do it within 24 months of release).

Which you want to use is not a simple question to answer because they provide different things. The LTS (12.04) should remain a stable, solid operating system but 12.10 (and then 13.04, 13.10 etc) will provide newer packages which may have improved features, perhaps at the cost of stability, though that is never by design.

If bandwidth is cheap and you have a bit of time, consider just testing both releases. Both ISOs allow you to burn to a USB stick and then you can test Ubuntu without installing it. It should let you know if everything works.