Hi Christine,
Your best options are probably getting either a Windows Mobile smartphone, a BlackBerry smartphone or a Palm smartphone. The term "smartphone" (rather than PDA) is more commonly used nowadays to better describe the all-inclusive and more advanced features that come included in these newer devices.
If you want to use it for emails and for surfing the Web, you may need to buy a data plan from your cell phone provider. But if you get a phone that has WiFi capability built-in, which enables you to use it to connect wirelessly to the Net from any wireless network ("hotspot") located in your area (office, coffee shop, home, etc.), then you may not need a data plan because many WiFi hotspots are free. Plus, WiFi connections are often faster and there's no bandwidth cap (e.g., no limit to how much you can surf the Web, send emails, download stuff, etc.).
Myself, I personally own an HTC Excalibur S620 (Windows Mobile) phone that comes equipped with a WiFi connection. I occasionally use it to surf the Web and access my emails. It's an older smartphone, but a great device that has a pretty loyal user base out there. Nice keyboard, lots of features and good support for it. These days you can get one off eBay for about $150 (brand new) or less. Plus I like phones that run on the Windows Mobile operating system because they have the familiar look and feel to Windows Vista/XP. Good phone for my basic needs.
Yann