Because of the two win conditions in skirmish battles, there are two winning strategies:
To decide which of these two strategies you should use, consider the relative strength and speed of your units compared to your opponent's. But generally, the most successful skirmish players choose to optimize their army for either strength or speed. Then use the corresponding strategy exclusively.
Note: Maps have varying levels of connectivity. Some maps have many working bridges between the nodes. Others have many bridges that have been damaged/destroyed and are not passable. Typically, highly-connected maps (fewer burned bridges) favour the speed strategy, while lowly-connected maps (many burned bridges) favour the strength strategy. This is because speed players rely on their ability to outmanoeuvre their opponent and the more intact bridges there are, the more ways there are to escape danger or move around your opponent's army.