Starting out, my first city (City Designer 3)

[Gandwarf]

Or should I try to keep using stone/rock to a minimum and use wood for the walls too?

It depends on the threat to the town and the wealth. If the town is under considerable threat and there is enough wealth, stone could be imported. There is a river, so the stone could be transported over water (the Egyptians used boats to transport stone to their building sites as well).

Also, do I need a gate in the north?

You have no road leading to the north, so I would say no. A gate would be an extra weak spot in the defence, so if it wasn't needed, it wouldn't be added.

If there are other towns and holdings to the north and this town trades with it, traffic would flow north and a gate might spring into existance.