Of course I now realize that in giving that advice you were ensuring work for professional painters in general, because clearly anyone who has tried to paint a ceiling like that will never, ever do it again (I hated it so much I'll be hard pressed to actually get the paint on!)

However, once I'm finished with the ceiling I'm going to be tackling the walls. Of course I've painted walls before, but it occurred to me that there must be a right and wrong way to do it, but I have no idea what those are.

I'm planning to use Aura paint (eggshell, I think). So far, I think I'm supposed to wash the walls with Dirtex, cut in with a brush and let that dry, then roll on the rest, making sure not to overwork an area when I'm rolling.

Anything else to it?

When I put on the second coat of paint do I need to cut in again or just roll?

Anyway, great choice on your selection (Aura). Just make sure you follow the directions for painting with Aura because it does begin to set up in a short period of time. You just can't keep rolling and re rolling. Need to roll it on and move on. Any little skippers you notice, leave along and you can get them covered in the 2nd coat.

You didn't say whether you have smooth or textured walls, so I am just guessing smooth here. I prefer to use Purdy's white dove dralon paint rollers. I use a 3/8ths or 1/2" cover. I also will de-fuzz the roller sleeve before using.
Get yourself a really good roller frame . You definitely don't want to use a cheap wobbly frame. I use Sherlock roller frame and also their very sturdy extension poles. When you get done painting all you have to do is tap the roller on the side of a garbage can or a 5 & the roller sleeve pops right off. Use an excellent brush for painting your trim. One that has a lot of fluidity and flow. If you are going to tape I would recommend using 3m- orange core delicate blue painter's tape listed as #2080. This is the only tape IMO. I would just make sure you have burnished the tapes edge down really secure. If you use any type of tool to press the tape down, you will need to be really careful about not poping a hole in the tape. Trust me it can happen. I myself use my index finger and lightly press the tape in place to get a seal and then I run my finger back across the tape really really good for the final secure. When you are finished painting, if the tape seems to be a little stubborn in releasing, take a box cutter or one of the craft knives to lightly score right where the tape edge is. This should release for you and don't remove at a fast pace. Remove the tape back onto itself.

Oh and with Aura , it would be a good idea not to have blowing air directly onto the work surface and if you have an outside wall that gets heated up I would paint this wall first. I am very particular about the temperatures in the rooms I am working in. They can make or break a paint finish. Another thing, if you don't feel comfortable or secure about using the Aura and afraid it will start to set up on you, I would like to also suggest using an x-tender for Aura. I only use XIM x-tender. Just make sure you follow instrustions and stir, stir, stir to make sure it has incorporated into the paint.

As far as washing your walls , sometimes that is overkill. In other words how long has it been, are there lots of spots or is the wall really dirty or just dusty, what finish is on the wall at the present time. If the walls are in good condition, just make sure you have dusted all over and if you had to make any repairs , dusting and removing all little flying debris. Washing walls and priming all the time is really ridiculous. Just have to thoroughly examine the walls to make the right determination. Yes, I would cut in the second time as well.
hope some of this helps. Good luck. :)

Just make sure there isn't any evidence of grease splattering, oils, etc. on the walls. I have painted ceilings before where grease has splattered up there and these are 10' ceilings. So yes we do have to be cautious.
good luck.

I have found MUCH more than just grease up there!