I ride dressage, and loose ring snaffles (either single or double jointed) are definitely the most common kind of bit used. They're mild bits and I've never had a problem with a horse not going well in one.
They can pinch a little bit- before I changed my bit, my horse wasn't showing any signs of discomfort while riding with a regular loose ring, but I could see that the corners of his mouth were red after riding. He has light pink skin, so I would guess it would show up more on him than on horses with darker skin. I ended up switching him to a "pinchless" style loose ring
and no longer see the corners of his mouth get red. If pinching is a concern for you, there are also companies that make a http://www.amazon
.com/Loose-Ring-Pinchless-Western-Snaffle/dp/B003LVNZPW of the pinchless snaffle, which are typically a bit thinner, and only seem to come in 5" single-jointed, but are also much cheaper. I looked into getting one of these to try before shelling out for the more expensive bit, but the only ones I could confirm the mouthpiece thickness were less than 10mm (the minimum to be show legal for dressage).
I've never used or noticed the nose strap being used, so I'm not much help on the combination part of your question