There are a zillion different PDA's out there made by many different companies. Sony, Palm, and Handspring are some of the more popular brands. About a year ago I picked up a Sony Clie and I love it, but there are many good ones so do your research to be sure what you are buying will fit your needs, and pay attention to Battery Life. Nothing is more annoying than having a PDA go dead just when you need it.
When it comes to the operating systems there are two main divisions of them - Palm operating system and the Pocket PC operating system. The brand name of the PDA will dictate the type of operating system installed, i.e. HP and Compaq will always use Pocket PC and Sony, Palm and Handspring will always use Palm OS.
The Palm OS has the most applications available for it BY FAR and most folks seem to like it better for that reason. The Pocket PC OS is decent but the applications really limit it. Palm is the more popular of the two and you will find many, many people write software for it to fit their own individual needs. Quite a few of these people are in the medical profession. Usually they make their programs available on various websites and charge very little, if any, money for them. This makes Palm the most versatile of the two.
Don't worry too much about compatibility with your home PC as either operating system will work fine with Windows, as long as you are running Windows 95 or later. Possibly Win 98 in some cases. Compatibility with your home PC is nice when it comes to scheduling using Outlook, synchronizing files that you are working on, to do lists, etc.
To give yourself an idea of what's out there for Palm try a search using your favorite search engine for Palm software. Contrast that to the Pocket PC. It's very unlikely that you will find any useful user written applications for the Pocket PC family. As far as I'm aware the only software available for the Pocket PCs is from the large companys out there that charge quite a bit and don't always have what we specialized people are looking for.
I hope this helps and it's not too much info. Feel free to email me if I can help you out further.