The Conexant modems, if I understand it correctly, are a variation of a "Winmodem" or "Softmodem" -- a modem where the majority of processing is performed by the host CPU, rather than the device itself. Compared to the original "hardware" modems of the past, these are much cheaper to produce, but also require a valid device driver in the host operating system in order to function. Winmodems tend to have drivers only for Windows, softmodems are perhaps better supported by a variety of operating systems etc.
Don't be so quick to judge linux based on this. Nonstandard hardware is difficult to support, especially if the manufacturers won't release documentation to the linux community.
Offhand, I'd say that your chosen distro, Ubuntu, really is above-average in terms of properly identifying and automatically configuring hardware. It's also a pretty good distro for beginners, in my opinion.
There's an excellent source for Conexant drivers (and a nice set of guides, as well) for linux here: http://www.linuxant.com/drivers/
Remember: linux is a different animal from Windows. Sometimes it might take a bit of work to get things just right. Sometimes it may require more--such as purchasing hardware based on the HCL here at LQ, just to verify you won't have a non-working peripheral.
However, once you get things running, you just might find it to be a more stable and reliable desktop environment. Don't give up just yet.