Well, you can use just about any ribbon you like. There are ways around resolving the grease issues. Some people line the back of the ribbon with tape or cut a same sized piece of clear contact plastic for the back of it. Others take a sheet of waxed paper, an old cloth under it, the ribbon on top and iron it. The heat from the iron causes the wax from the waxed paper to adhere to the back of the ribbon and the wax stops grease spots from coming through.
Satin ribbon is the worse for grease spots, but some of the polyester satin ribbons are fine. A lot depends on the type of icing and the room temperature.
I like the organza wired ribbons the best as they are easy to work with and yet are still a bit transparent. Of course any wired ribbon to me is just great! You can use double sided tape to join the two ends from underneath. Some folks put a straight pin, the hat type with the pearl end, through and overlap the joint. Others make a bow or loops at the joint so you don't see a seam. You can also use a glue gun to adhere the overlapped ends together.
Always wash and dry and iron if you have to, any ribbon you use.
Generally I do a test run, take a bowl of a bit of icing, put a tiny piece of the ribbon on top of it and leave for 24 hours and check. That way you will pretty well know how it will react.
If you put a white ribbon in a red cake, well expect some colours bleeding out to be an issue. So put a backing on your ribbon. I have even used interfacing if I had to. Or that iron on stuff you use so you don't have to sew a hem, hem tape I think it is called.
I am not too keen on the ribbon that bows you buy from card shps are generally made of. So I don't use that kind.
Generally you can use any ribbon, lace, cording, binding, or trim you can find.
Hugs Squirrelly Cakes