Eh, I think the ADSL modem itself shouldn't be a problem - I don't think you'll need any drivers for that. I assume your tablet PC has a built-in wireless adapter - that might be the one that'll give you more problems when installing Linux, because the product companies don't always provide the Linux drivers. Cue mad Google searching for generic drivers, or digging for info on the wireless adapter (e.g. which chipset it uses - leading to the drivers for that chipset), etc.
If I were you, I'd surf for info on whether others have had problems with running Linux on that tablet PC of yours first (specifically on the wireless adapter issue). If the tablet PC is the only PC you have, then this is all the more important, because the worst case is to encounter problems and be unable to surf the web to find help / info.

As for the operating systems, I've only used (sparingly) Ubuntu Linux on an old desktop PC I had (not anymore though). I think it's one of the easiest to install, and the package upgrading support is pretty good. Fedora is a pretty simple install too, but I haven't used it much. Ubuntu also has a pretty decent support community out there.
If your XP is working fine, then personally, I wouldn't advise reformatting it off and installing a new OS which you (I assume) have no experience with. Probably safer to just install Linux on top of it (if you've disk space) and dual-boot (so you can choose at power up, whether you want to boot into Linux or XP). That way, you get a chance to try out the new OS without losing access to your PC, if things go wrong.