Start with single player, for sure. Multiplayer, especially online multiplayer, raises a whole slew of issues that just do not occur in single player.

- Keeping all clients in sync. Each client should only know the parts of the game state that are relevant to it.
- Coping with lost, duplicated or out-of-order data packets.
- Coping with clients dropping out.
- Coping with the server dropping out. Do you terminate the game or does another client take over, ie. host migration.
- Dealing with network latency. This may be such an issue in a turn-based game. In a real-time game, latency can be a killer.

...and this is just the beginning of it all.

Having said that, most games that support single player and multiplayer provide single player as a one player multiplayer game. That is, the single player client is the same as a multiplayer client. The server is still there an operating as normal in the background.