Internet from a high altitude balloon is only going to happen with a suitable satellite modem. It'll be slow and/or expensive.
Which leads me to .... what is it that you actually want?
For the most part, hobby weather balloons just send down position data (telemetry) and perhaps images too. APRS is possibly an option however you will need a ham licence, and you will only be able to launch in or fly over a country that allows airborne amateur radio transmissions. The USA for example is one such; the UK is not.
APRS is bi-directional though for balloon use it's pretty much always used for transmission only from the balloon.
If APRS is not an option for you, then there are some ISM (e.g. 434MHz in Europe) transmitters and these are typically used with RTTY encoding and a ham radio receiver on the ground. Telemetry and images can be sent (albeit image transmission is very slow). Don't buy a matched transmitter/receiver pair as these typically use high data rates meaning that the maximum range from balloon to ground station will probably not be enough to track the balloon throughout the flight.
I suggest you start at the UKHAS wiki (
www.ukhas.org.uk) as this is a wide subject and you need to do plenty of reading to make sure your flight is a success.
Dave