The only roads you will ever REALLY need, in order of priority:
1. Roads for trade network. Make use of rivers! A resource near a river can be connected by just building a road to the river. For resources right beside the river, you only have to build a road on the resource itself to connect it.
2. Roads to connect cities.
3. Roads to speed movement of units to the front.
That should be all you need, although there are a few exceptions. For example I often build roads on every tile in my border cities so that the city garrison can respond quickly to any pillagers the ai sends.
1. Roads for trade network. Make use of rivers! A resource near a river can be connected by just building a road to the river. For resources right beside the river, you only have to build a road on the resource itself to connect it.
2. Roads to connect cities.
3. Roads to speed movement of units to the front.
That should be all you need, although there are a few exceptions. For example I often build roads on every tile in my border cities so that the city garrison can respond quickly to any pillagers the ai sends.