2) A good top coat. A lot of people have touted Seche Vite as the be-all end-all top coat, but I have my issues with it. For one, I feel like it gets gloopy about half-way through the bottle, and then you need to purchase their polish thinner in order to get the consistency back to normal! I think that's ridiculous. I think the Essie Fast Drying top coat works just as well, and it really is "fast-drying". It doesn't get gloopy quite as quickly as Seche Vite.
3) Color! The draw in doing your nails at home is to have a good array of different shades and colors to choose from, like you would at the salon. It makes changing your manicure every couple days fun & something to look forward to. I'm not saying you need to have a fully stocked rack like mine.... But it helps ;)
5) A cuticle pusher or clipper. I think a cuticle pusher and/or clipper is essential. Not everyone likes removing their cuticles with a clipper, but at least invest in a pusher. I don't even take care of my cuticles every time I do my nails, but every once in a while it's important to push them down. It makes for a much cleaner manicure.
6) A multi-sided nail file. This multi-sided nail file is great. It serves so many different purposes. I use the extra-coarse side to file down my nails after cutting them, and the file nail edge to dull down the sharp finish of a freshly cut nail. If you have nail ridges there's a handy "smooth ridges" side to help you out.
7) Hand cream/cuticle balm. It's important to keep your cuticles healthy by using a hand cream or cuticle balm on them every so often, especially if you tend to pick your cuticles (bad habit!) or if you have dry hands in general. It'll make your manicure look so much better.
As a final point, it's important to practice! As with anything in life, doing your nails well requires repetition. If you do them often enough, you'll become good at painting nails even with your non-dominant hand.