Historical data format is the same as provided by real-time Bitstamp WebSocket v2 with addition of local timestamps. If you'd like to work with normalized data format instead (same format for each exchange) see downloadable CSV files or official client libs that can perform data normalization client-side.
Tardis-machine is a locally runnable server that exposes API allowing efficiently requesting historical market data for whole time periods in contrast to HTTP API that provides data only in minute by minute slices.
Bitstamp real-time WebSocket API does not provide initial full order book snapshots for live_orders and diff_order_book channels subscriptions. To overcome this issue we fetch initial order book snapshots from REST API and store them together with the rest of the WebSocket messages. Such snapshot messages are marked with "event": "snapshot" and "generated": true fields for respective channels.