Hi Paul
The phones gotta be equipped with SIMs that are on the 3G networks if you want internet access
The term "wireless internet" can be quite confusing/misleading to ordinary folks - you can get wireless internet connection via your telco carrier eg; Telstra, 3, VodaFone, Optus etc - so you get an mobile internet by using your new phone to connect to the web directly using the phone's WAN (wide area network) capability thru the telco's 3G network - this type of connection costs you air time (basically a mobile call) - ie whatever the going rate your telco charges for mobile calls, so if you're downloading large amounts of data then expect a big bill
On the other hand your new phone probably would also have wireless LAN (local area connection) connectivity and this allows you to wirelessly connect to a LAN network (of course that network has to have a wireless access point for you to connect to it!) and from within that LAN consequently connect to the internet (ie assuming that the LAN is already connected via ADSL landline to the internet) - An example of a wireless LAN type connection would be the freebie wireless connection at most McDonalds - you can use your phone's LAN connectivity to connect to their wireless hotspot access point and then you can surf the internet - this LAN connection does not cost you air time = FOC
In Europe there are lots of places where wireless LAN hotspots are available to use FOC if you patronise the business and therefore you can use your phone's wireless LAN connectivity to connect to the hotspot access point and hence gain access to the internet - in case you have to pay, that's fine too because you are only paying the business for the rates they charge for a timed block which you choose and not using your phone's WAN connection to get online (if using WAN overseas it means that you have to get "roaming" enabled on your mobile service and essentially it means that you are actually making a mobile phone call = very, very expensive!)
Sorry that this is a bit long-winded but I did it for clarity
HTH
Cheers
Bill