I tend to agree with TFJ. By the 6th Ce Rome was gone in the west and most "barbarian usurpers" would have looked similar (especially Nobles/Bucellarii) in my opinion. I think the big difference with Byzantine horse is that they would have looked more uniform with both spear and bow armed cavalry.
My Byzantine Army is all Essex and I like to peruse their site for pics when building an army. For the rules I use my cavalry are based with spears in front and bow armed horse behind. I also have spear armed horse mixed with bowmen in between, or all spears, on smaller bases. My Byzantines also have plenty of light horse (bow & spear) which is something you usually won't see in most "successor states".
In my opinion Byzantine Cavalry was their best troop type at this time so only my front rank of spears would wear mail with bowmen supporting as a possibility, but not a given.
I think Ostro/Visi Goth spearmen with late Roman Aux types mixed in wouldn't look out of place.
I don't think a Frankish Army would necessarily look Frankish at this time. Burgundi, Alammani and Thuringians were all absorbed by the Franks in the 6th Ce.
I think an East Roman/Byzantine Army is a good place to start for this time period. Enemies include the Sasanians, Gepids, Franks, Slavs, Ostrogoths, Visigoths, Vandals and Avars.
Best of luck with your project.