My understanding, and I use this on my Blackberry is that when you connect to the internet by just clicking on the icon on your phone you are receiving it via the 3G network - the cost of doing this is included in your "package" and you need to check what your limit is.
Using the wifi option is for local area connections to wifi hotspots/home networks etc when you will be using the private internet networks - if you connect to your home router, for example, or a router in someone else's home, you will be using the broadband connection and no extra costs should be incurred. When you connect to a wifi hotspot in a public place you may or may not have to pay. If you have a set limit on your phone's 3G internet provision then it would be more economical to connect to the internet by wifi whenever you can.
The beauty of having an internet ready phone is that you can tether it to a laptop to receive the internet on the go through the mobile 3G network - again this may or may not mean that you will have to pay a "bundle" charge - I have to purchase a bundle when I take my laptop abroad and connect this way with my Blackberry (it can be expensive so is only used when really necessary.
Hope this helps - and hope I have explained it properly. All works for me this way anyway.