I have successfully taken rose cuttings with both new and old wood. It is important to let the new stems sufficiently mature. The new wood is usually mature enough after the stem has just finished blooming. If you don't let the stem mature enough, then it usually becomes limp and will die before you can get it to root. I take cuttings from new rose stems in the spring right after the first bloom cycle. Then in early to late fall (in Southern California) I prefer to use more mature or old wood. When using old wood in the fall, I will remove the rose cuttings from the Mason jar, baggie, or mister, after only several weeks since it is cool enough then for them to root on their own as long as I water them daily.
It is generally agreed that "old roses" include species or wild roses; albas; Bourbons; moss roses; China roses; Noisettes; Portland roses; rugosa roses; Scotch roses; centifolias; hybrid pimpinellifolias; damasks; gallicas; hybrid perpetuals; tea roses; and musk roses. Those classified as modern rose varieties are hybrid teas; floribundas; polyanthas; grandifloras; miniatures and dwarfs; modern shrub and landscape roses; climbers and ramblers; and rugosa hybrids.
There will be disappointments along the way, when many rose seeds fail to germinate, or perhaps they do germinate, only to die several weeks later from damp-off disease. Sometimes a rose seedling will turn out to be as ugly as sin, or very sickly, and you will reluctantly have to throw it away. Other times they will be just ho-hum, or look too much like its parent, and therefore have no value. But, just when you don't expect it, you might discover that one of your rose seedlings turns out to be very special.