To get your sound, there is simply a checkbox in the export panel that reads "export soundtrack". This is assuming you have all your sound on the TVpaint timeline. It will probably matter to what format you export as well. You want to make sure that your sound format is compatible with your video format. For example, certain uncompressed AVI codecs would not allow MP3 or MP4 sound to go with it.
To get your film on the web, you have a number of options, depending on whether you want to control everything yourself or use a video sharing service like Youtube or Vimeo. The sharing services will likely handle everything for you. You simply upload your finished video and they will encode it and then give you "embed codes" that let you stick the video in your own webpage. If you want to control everything yourself, some other techniques will be necessary.
If you are creating video for your own page, I believe MP4 is the format of choice today. You should be able to export this right out of TVP and even shrink it to your desired size, right in the export panel. With Mp4, you can use MP4/AAC sound as well, which will keep the file size down. Depending on whether you are on a Mac or PC, you will have different options, or at least a different looking panel, for choosing your data rate, which will determine how big the file will be, and other aspects of the final video. Since very few people could stream a 1920x1080 video, you could, for example, export at 640x360 with a data rate of 512Kbps and get a great result.