Welcome to the Forum. I currently have a 7250 with Verizon. You are able to access the internet as long as you have a data plan. You are able to access as long as you have a data connection, which I think is just the equivalent of have wireless service.
As for the battery life, obviously that would be a person by person evaluation. I use mine all day, receiving e-mails, text messages, cellular phone calls, and accessing the internet a few times a day. I have yet to see the battery strength meter lower than 2 or 3 bars.
Good luck and from my short experiences so far, I think you will love the wireless services and the Blackberry 7250.