I own a drywall company...
A piece of advice on the ceiling flats. When doing the tapered seams you are looking at a tape coat, a fill coat, and then a feather coat. The feather coat is best done with "topping compound." On a level 4/5 finish, which is what you are looking at on a flat black ceiling, you will want to pull the mud past the normal 6" taper built into the drywall. I use what is called a "flat box" on seams and I'll wipe all of my tapered seams with at least a 10" box with the crown set flat.
To do these by hand once the seam if filled use your 12" knife and pull a loose mixture of topping compound over the entire tapered seam. Once dry, go over the seam with the 12" knife setting it perpendicular to the wall to look for high/low spots. I use this sander, called a "radius 360."
On the dreaded "butt" seams I make my joints in the "field" by using butt splicers which are nothing more than thin OSB ripped to 4". This prevents the natural crowns that always exist in floor joists and trusses from negatively affecting your seam plus it gives you significantly more area to screw to making a stronger joint which leads to less cracking.
When doing your initial tape-coat on the butts make sure you wipe the seam fairly hard and make sure you ALWAYS thin your All Purpose mud when taping. This helps to insure a good bond between the tape and the drywall and keeps the tape bump as small as possible. Avoid using fiberglass mesh tape like the plague. It has it's place - but it's more difficult to work with.
Once your initial tape coat is fairly dry take a 10" knife and make two swipes along each side of the seam meeting in the middle of the tape. Don't worry about covering the tape at this time though and don't over work the mud. Lap marks are to be expected - they sand off very easily once dry but you'll create more problems if you try to work them out with your drywall knife. You are trying to build up the angle on each side of the tape. Once these two "stripes" are dry take a 10" knife and fill the crater in the middle. Let that dry and lightly sand - your butt seam will be flat to the eye with very little sanding.
The above technique is how professionals get flat butt seams using "flat boxes" but you can do it with standard drywall knifes as well.
Many professionals will, when dealing with a level 5 finish, spray the entire wall or ceiling with thinned down drywall mud through a special sprayer almost like paint.
When painting a smooth wall be sure to use proper painting techniques - don't try to eek out that last bit of paint on the roller. This leads to tiger striping which can be seen.
Below is a pic (not mine) which shows lap marks and the proper method to feather out the butt seams. This was done with a flat box but you can achieve similar results with knives...
Notice that the tapered seams extend past the 6" taper...
On edit... I always buy my mud in boxes and mix it with some water in a bucket. This gives you butter smooth mud with no chunks and an even consistency which is important. When you are done working for the day clean the side of the bucket all the way down to the level of the mud (in the bucket) and pour enough water into the bucket to completely cover the mud. This is called a water cap and it eliminates crusty mud from getting into your working mud. When you are ready to work again just pour the water off and re-mix your mud.
There are a ton of pics and videos on the web that show how to finish drywall but you really just have to do it to get it...