There is no 'appropriate' level for a commander of 3000 cavalry. But, there are things that may direct your thinking.
What is the force's role and current mission? Is it on extended raiding? Is it mostly garrison? Is it on extended campaign? How far will it be from home bases?
If the force is on extended campaign away from home bases and the commander does not have good logistical/administrative skills, then he'd darn well better have someone in the force who does. It's possible that the nominal commander might command from the front, but if so he's mostly just going to be someone who plans out strategy before the conflict and then rallies people at the front lines rather than makes judgements about the development of the battle and changes of plans. He had better have a core of officers who do hang back, collect information from the wings of the battle, and then have the authority to issue changes in orders to make necessary adjustments.
What is the role of the military in the society and how does one excel in the military?
If the society is meritocratic, then you should expect that the commander is qualified for the job with the necessary skills to manage 3000 horsemen. If officer posts are appointees from the nobility, these skills may be considerably lacking and the commander might not be very good at all. In the meritocratic case, the commander would probably be a fighter with a few expert levels. In the latter case, he's probably all aristocrat.
How bureaucratic is the military? If highly bureaucratic, each unit probably has specialists whose job it is to lead on the battlefield (mostly fighter, some aristocrat, maybe some expert), direct from an overview position adjacent to the battlefield (fighter+expert or aristocrat), handle logistics (mostly expert, some fighter/aristocrat), and all that. I would submit that the overall commander of the force is most likely to be in the overview position. Any other place would dilute his authority (caveats for having a very trusted officer corp in this position) because it would be someone from that overview position who would be issuing battlefield level orders once the fighting starts.
Note that the Romans would be highly bureaucratic with a mix of meritocratic and appointment. As a result, they were darn effective users of their military technology much of the time, especially with respect to routine operations (nobody sets up camp like the Roman army) and when their appointee commanders were actually competent or very lucky (or both in the case of Caesar).
The WWII Wehrmacht would be highly bureaucratic and meritocratic early in the war, more appointment-based later on (as Hitler gutted the competent officer corp that bucked his authority). As a result, they were very effective at times, and very ineffective at other times (such as when you put a staff officer like von Paulus--more of a logistical expert--in charge of the whole 6th Army and waste them at Stalingrad).
Most medieval armies would have been very much along the appointment/ aristocratic rights line, especially the cavalry. They may be effective against similarly organized bodies, but against a bureaucratic/meritocratic organization that is well supplied? They're probably screwed.
Would the commander necessarily be the best fighter?
No, almost certainly not. Even if he does lead from the fore, chances are he's not spending as much time fighting as some of his more elite units. Even at the front he'll be running around probably helping stiffen morale. Of course, you could argue that increases his life expectancy (snipers not being nearly as common in the medieval mode as they are now) and enable him to build up more levels in the long run than his troops (even if his troops advance more quickly).
