Welcome. When Apple introduced the iPad 3 this year they kept a basic iPad 2 in the product lineup as an entry level model. Assuming you're buying new, then the iPad 2 is only available as a basic 16Gb model, whereas the New iPad goes up to 64gb. More storage space means you can carry around more movies, music etc... If you don't expect to keep much with you on the device, then 16Gb may do, otherwise go for something bigger; FWIW I have 32Gb and the only time it ever gets close to being full is when I load it up with films for on holidays. The New iPad also has a better screen then the iPad 2 (not that the iPad 2s screen was bad!) and significantly better cameras.
All iPads come with WiFi to get online, and models are available with 3G as well; to use 3G you'll need a microsim from one of the mobile phone carriers, and some kind of payment method - contract, PAYGO, whatever. Here in the UK we're fortunate have a very broad range of options from all the national carriers; I only really use 3G for syncing contacts and calendar entries, and occasional very light browsing; I use Orange, as they had the best option for a low user like me when the first iPad came out - no contract, pay for what you use by direct debit at the end of the month, and capped so you don't get any surprises; other carriers may have similar offers, but I haven't looked recently.
If you haven't already done so, then it's probably worth having a trip to your local Apple Store to compare the different models.
Hope this helps, Pete.
