Sunny - sorry I haven't answered your question, haven't been around much ( must finish skaven army, must finish skaven army, must……….). for Varangians, basically see Normans. However, the big differences were the shield and the top armour. The varang shield is about half the size, but same shape , as a norman 'kite' shield. The two edges could be bladed, and it could be fixed to the arm, leaving the hands free for a great axe. The armour is tricky. It looks like a lamillar or scale armour body worn over a mail hauberk, but I'm not so sure. That is an incredibly heavy combination, so I think the mail was probably just sleeves and a skirt or kilt over the legs, attached to the main body.
The Byzantine touches would mostly be in the decoration , particularly gold medallions and plating - The biggest change would likely be the style of cloak - shoulder fixed rather than wrap around and brooched - possibly Eastern style embroidery on edging or shirt sleeves? Material would be lighter, less wool, more cotton, or silk if a noble. As an officer, the helmet would be decorated, probably with a horse hair plume in a regimental colour.
Weapons - my field. The great axe, same as the saxons, was the primary weapon. These things are awesome - a good stroke can decapitate a horse. They would also carry a sword, probably a Gladius or a Greek Kopis, but maybe a Viking round tip ; and a dagger or seax. Some used bows, but that is a whole can of worms as to which type.
Hope that gives you some pointers, and if your other costumes are anything to go by, I can't wait to see it.
@hairyjeff Thanks

I was actualyl thinking, maybe you could help me out with some costume questions for LARP (Viking age) ? I'm playing a Chieftain who has come after serving as a Varangian Guard and I wanted to have his costume as an exotic mix of Viking and Byzantine/Greek clothes. Any ideas?
addendum. I have been told that the helmet was a rounded bowl with a nasal guard, or possibly a mask, over the face; not as pointy as a norman helm, which evolved from the varang. Didn't know that!