I like glass nail files, but the emery board ones that are a bit thicker (like this: www.wilko.com/essence/essence-profi-nail-file-4-in-1/invt/0400864) are also good.
I usually cut my nails with a pair of nail scissors and then file them so they have a good shape and don't have any sharp/scratchy edges. You can just file them until the length and shape is right.
I like when they are not too long - a millimeter or 2 longer than my finger is fine with me. My mum was told this was the acceptable length when she worked as a stewardess back in the day and I guess it stuck with me. It looks feminine but not too long. At that length they also seem to not break too often.
Marylou2 is completely correct about Dior Nail Glow. It's lovely and very natural. And the brush is lovely - it has a good shape.
If it's a bit above budget, especially if you're only planning on using it once, then a clear nail polish from any brand should do fine.
If you are right-handed, then it will probably be easier painting your left hand first. Position your left hand so you do not have to move your right hand too much in an awkward position. I like placing my thumb on a slightly raised surface (a book, small box) or placing it just on the edge of the table so the rest of the fingers are below the tabletop.
When doing the other hand, again make sure that the hand doing the work isn't in an awkward position as it can be hard to control.
You should wipe some of the nail polish off the inside of the rim of the bottle (so it runs back into the bottle) as you might find that too much polish on the brush will run onto the nail and finger in a big blob. I usually just wipe one side of the brush, and the side of the brush with polish on is the one I use on the nail.
You can always get more polish on the nail by dipping the brush into the bottle - it's a bit harder to get too much polish off the nail.
I use this method when applying the polish: www.nailpolishforum.com/forum/richedit/upload/2kdaee743d4c.jpg
Leave to dry for 10 minutes before doing anything that could dent the nail polish. If you apply a second layer, wait 10 minutes before applying it and when you're done, wait another 10 minutes.
If you're not used to doing your nail polish, then leave one hand to dry completely before painting the other - just to avoid denting the polish you've already done. When you're used to it, you're fine doing both hands with wet polish.
If you get polish on your skin, then I find that the easiest way of getting it off is to wait until the nails are completely dry, and then scrape it off carefully (you can use a manicure stick, a nail brush, an old toothbrush or whatever you have) while having a shower/just having washed your hands in warm water or if you've applied hand cream and left it to sink in for a bit. It just peels off.
I've never been had a professional manicure so I can't really help with that.