Private study is precisely that - you're supposed to stay on site and study somewhere - or you can play cards etc.
The summatives are practical exercises using a radar - you control a/c in the airways and outside controlled airspace. You have an airfield in your sector which you'll need to vector inbounds onto the ILS and deal with outbounds.
You get to state your preference towards the end of basic. Rumour has it that your preference is the last thing to be considered, if it is at all, when they make the streaming decision.