But with Freeserve (I hate the name wanadoodoo)you have to connect everytime you have turned your computer off.
Once you have connected it will stay on until you either disconnect it yourself or Freeserve disconnect you (they sometimes do this but you can re-connect immediately)or if BT run a test on the line.
Sometimes if an external agent such as this has disconnected you I have found that the right hand light on the modem will keep flashing. This might only be the way I have it set up. But if this is the case simply re boot the computer.
Regarding the speed of your connection: I am connected within seconds and always have been but I am quite close to the exchange I don't know if that makes a difference.
Hope this helps.