If you are redecorating your living room, it is a great time to add a bit of color to your room, and red window curtains are a great way to do that. Red is not an easy color to add into an existing room as it is quite a dominant color, but if you are designing your room from scratch it is a great color to work with.
The main thing before you choose curtains or curtain fabric is to have an idea in your mind of the kind of room you want to create, in particular, whether you are aiming for a contemporary or traditional style. There are window curtains which will suit either of these styles but, in general, what will suit one will look wrong in the other.
A contemporary room needs bold splashes of color or bold designs incorporating just a few colors. You can achieve this with solid red curtains or by finding a large scale pattern, which includes the shade of red you like. With this kind of room, simple curtain headings without gathers are best and tab tops will look particularly good.
If you are leaning more towards choosing a traditional room design, then patterned red curtains will look better than plain ones, unless you are considering a very rich fabric, where the texture of the fabric has a traditional feel. Damask or velvet curtains would work well, for example. As for any pattern you choose, it should be on a much smaller scale than for a contemporary room. For instance, for either of these style rooms you could choose floral curtains, but whereas, for the modern style you might choose a giant flower print, for a traditional style, small roses with foliage and other blossoms would look better. When considering curtain headings for your traditional room, keep these standard too. Various types of gathers such as classic or pinch pleat will look good.