I understand that you need some assistance in order to know what to buy.
First, the Slingbox SOLO and the Slingbox PRO-HD will allow you to send the TV signal out to the Internet. The main differences are that the Slingbox PRO-HD will stream the HD signal and the Slingbox SOLO will allow you to stream the HD channels but on Standard definition (SD). Besides, the Slingbox PRO-HD supports up to three supported devices and the Slingbox SOLO supports only one device at the time.
The following links will provide you with all the details about these devices.
If you want to send the TV signal out to a TV set, you will need to get the SlingCatcher, since this device allows to achieve this specific task. The Slingbox does not have this capability per sé. However, since the SlingCatcher is no longer available, you'll need to track it down through the Internet. The following link will provide you with all the information about the SlingCatcher.
You must also know that the Slingbox will allow only one connection at the time. This means that you cannot send the TV signal out to multiple TV sets at the same time.
There are Mobile applications that will allow you to get the signal on your Mobile devices. The following links will provide you with all the information about the SlingPlayer for iPhone and SlingPlayer for iPad.
Even though both devices are attached to your Sling Account and App Store account, you must purchase the application for each.
Finally, you must connect the Slingbox at home to your network and TV source (cable box, DVR or satellite receiver). Then, you'll need to run the Setup Assistant for Internet Viewing. This process will allow you to send the TV signal out to the Internet and you will be able to get the remote connection through the Mobile applications.