If a PDA is WiFi enabled, will it be free to use internet?

I was hoping to have all of the benefits of scheduler etc. --plus web surfing & email--my friend suggested I get a smart phone, but I don't want the additional expense of increased monthly bills. I thought a PDA would be the way to go. But, friend tells me I will have to pay for internet use on PDA ("nothing is free, you know..") so, I might as well have gotten a smart phone. I thought Wi Fi was free. What is the real story on PDA's and WiFi???