I did see that art on @joannalannister‘s page, it was very cool.
The standard bearer is there to make sure that everyone else knows/sees where to head towards in the chaos of battle, and to motivate them to keep going, because it was considered a huge shame to allow your standard to be captured in battle.
As to how the standard carrier fought, they had a sidearm, but sometimes they would use the lance the standard was attached to.
In terms of household knights, Tywin’s 500 was seen as a surprise, but a younger brother like Kevan has 200 under his command and pretty much everything baout Kevan is conventional. So for a Lord of Casterly Rock, somewhere in between there is more typical; Tymond Lannister arrived at the Great Council of 101 AC with 300 bannermen plus men at arms, so take that as you will.