Prior to polishing my nails, I use the same set of products every time I do my nails. The products I use may not necessarily work for you and I'm in no way saying it has to be done exactly like this.
First of all, I remove any polish and oils from my nails with Onyx Professional 100% pure acetone (the clear bottle with the black cap. There is also the pink formula, but I prefer this one). Acetone is completely drying and is harsher but it works the best for me. I feel like I also use less product to remove and it easily removes harder polishes and glitter.
After my nails are completely clean, I nourish my cuticles with CND Solar Oil Nail and Cuticle Conditioner. I take a drop per finger/nail and massage it completely into the nail. Because I change my polish once...sometimes even more per day, my cuticles are really damaged. This is also currently helping with hangnails and rough cuticles.
When the oil is completely massaged in, I wipe off the excess. I then file them and fix the shape of my nails. I also will go in and cut them if necessary.
Then I apply OPI Original Nail Envy nail strengthener. I've tried a ton of different products. This has worked the best for my nails since I removed my acrylic nails. In general, I don't like having long nails so I can't really say whether or not it makes them grow ridiculously fast. But this has really strengthened my nails and they are noticeably thicker and I have very little problem with them breaking. I do on occasion ding my nails on counters and other objects...but that's going to happen with whatever product you you.
After I use whatever polish I decide, I top off everything with Seche Vite. I've heard both good and bad things about this, mainly about it being toxic and the ingredients being harmful. This is what I have to say to that....I don't sit in a bathroom and smell the fumes. I paint my nails in well ventilated and open area. This top coat is by far the fastest drying and protects my hard work from chipping. Any polish is toxic if you inhale it constantly. As long as you're careful and are conscious of what you are doing, you'll be ok.