It sounds like you are looking for a PDA that can access the internet via WiFi, the primary source of wireless internet. Basicly, any PDA with WiFi would do for your needs, but it's best to make sure that you will be able to use it.
In order to use WiFi, you must be within 75-150 feet of the source of the signal. Thus, you'll be able to access the internet only if you are at home or work (and they have a wireless network), or you are at a public ''hotspot''...a location where WiFi access is available. Sometimes these are free, and other times you must either be a registered customer or pay per use. Also to note, not all webpages can be displayed properly on a PDA.
If you wish to access the internet from all locations (on the subway, at a restaurant, etc), it may be best to look into using your cell phone for accessing the internet...either directly, or using another wireless technology called Bluetooth to access the internet on a PDA, and use your cell phone as your connection. This way you could access the internet just about anywhere. The downside is that the connection speeds are much slower, and you have to pay for each connection, as it would count towards your cell minutes.
Let us know when/where you expect to access the internet, and we'll be able to provide you some more advice.
Hope this helps,