That is perfectly normal new growth on a healthy and happy new rose! Congrats! Enjoy!
Seriously, MANY roses have red new growth that turns green as it matures. Also most all thorns do start out soft and harden up as they mature. New growth is always a bit tender to begin with. Your rose looks very good and I don't see anything here you need to worry about.
Do you know the name of the rose? Post pictures when it blooms, please!
