After removing all nail polish I usually go right into my cuticle care. I use a variety of methods to remove had or unruly cuticles nothing specific or any one brand, just whatever I find that works.
I bought this one at Big Lots a couple of months ago and have been really impressed with it. It removes cuticles quickly and easily with no problems. Just brushes on and wipes clean.
I also recently purchased this one but I am not sure where, I think maybe Walgreens. It is also pretty good at removing cuticles without having to use clippers. It comes with a little cuticle pusher as the tip on the applicator but I find it messy when I try to use it.
Here we have an oldie but goodie, I have had this at least 5 years and it still works well to soften and lift dead cuticles. Now you will need to push your cuticles back very well with this one as it is not as potent as the other two.
Cuticle oil that I have also used for about 3 years, I use this about two to three times a day. Don't really notice much difference, but it is supposed to be really good for your cuticles.