What's the difference between 12.04 and 12.10?
12.04 and 12.10 are two different releases. They're named based on the date (April and October of 2012, respectively).
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.
In addition to Oli's great answer:
If you are new to Ubuntu and wish to "just use" the operating system rather than play and experiment with it (e.g. if it is for business), go for the long-term support (LTS), i.e. 12.04 LTS. You will not have to upgrade until 16.04 LTS (April 2016), although you would probably want to upgrade when 14.04 LTS comes out.
(LTS versions come out every two years in April.)
If you prefer the latest software, and playing and messing about (as many do), go for the latest version.,Be aware that you would need to upgrade every 18 months at a minimum, although you'd probably prefer to upgrade every six months.
Note that you can always upgrade to the latest software (selectively) even if you decide on 12.04 LTS, so you can have a mix of the best of both worlds.
Your question might be coming from the fact that 12.04.x is long term while the 12.10 is "normal term". For what I have read, you are the typical end user for Ubuntu, so you will most likely enjoy more the benefits of having the latest version of Ubuntu (The 12.10 right now) instead of the more stable version of Ubuntu with longer support (The 12.04.1).
It might sound weird since I know you want the newest but also the stability and support. Do not worry about this since 12.10 also has it, but the long term support versions are mostly made for types of users that want to stick with one version of Ubuntu for a long time, one to start/create a server or want something that will have support in case of worst case scenarios (Like the same server caught on fire or something).
For the normal user like you and me, the latest will always be the best because:
You have the latest, tested Linux Kernel. Which means you have more device support, better drivers, new technologies, etc. This will also go to a long term support version but only after a lot of testing.
You have the latest updates for, as an example, Unity, Compiz and other GUI tools (Like LibreOffice, Empathy, etc..)
Since you are into programming, 12.10 has an updated list of GUI apps like Codeblocks, Eclipse and others. Installing services like Apache or MySQL is the same in both cases (12.10 or 12.04.x) but they are more up-to-date on 12.10.
12.10 has less errors since it is based on the knowledge and software from 12.04. Of course, since 12.04 is a long term support, it will backport any enhancements from 12.10 to it.
The only downside from using a normal release like 12.10 would be than when the new version comes out, like 13.04 in April, you will most likely need to update to it to keep up with the latest and greatest (Assuming you want this), which I would recommend since 13.04 packs too many good features to name here.
At the end is your decision to whether go with 12.04 (Stability and more checking) or 12.10 (Latest fixes and enhancements, etc..)