I know it's a lot more involved than that. I've been all over the forum looking for a book and or info on the best way to cut up a log so I get the most usable lumber. I will be cutting western red cedar, fir, and pine. Did I miss it? Or am i just blond ? 
But you got to have a personnel relationship with your mill and that takes awhile.
Calaveras County, huh? Do you do frogs?
What kind of mill? I'm a circle sawyer and know very little about band saw sawing so what I say is FWIW.
A lot of your questions are only going to be answered with experience but we'll try. You might look for somebody else in the area with a sawmill and offer to help them for the experience. Mostly small mill owners are a subspecies of people and tend to get along. All that I have found are willing to help. I'm sure there are a few A-holes out there but they are rare.
What's inside a log varies with species and geographical area and even growing site. Every log is different. How to cut the log also depends on the type of mill you have and what you're trying to get out of the log. Lots of "depends".
Western red heart wood has good rot resistance. Can be used structurally and great for picnic tables, shingles, fence posts and rails and siding/sheeting. High dollar wood where I live. You probably also have Incense Cedar. Big difference. Incense is also known a pencil cedar because that's a major market for the wood, mostly used in appearance grade applications, picnic tables count. Either can be used for studs and such but there are better uses. For structural strength look to your pines, (but not Ponderosa) and D. fir and any of the true firs. Ponderosa is used mostly as appearance grade like knotty pine. Any of the woods you have, if massive and/or oversize, work. Check with the local builders.
As Kirk said generally keep the heart centered in posts unless you have large tree that can be cut without any heart center. Boards from the outside posts from the centers.
Keep the grain straight (
slope of grain in the grading book). On smaller trees if your saw blade enters the log say 8" from the heart center you want the blade to exit the log the same distance for the strongest boards. Said another way, a particular grain on a board should stay within the board from one end to the other. The spec is 1" in 12" or 1' in 12', but I think that is way too much. Cross grain boards tend to fall apart.
On larger trees cut parallel to the bark to get the best wood and then make a correction toward the center. What I consider perfect is if I can saw the pith (heart center) out with the saw kerf. Haven't hit perfect yet but that's the goal. But I haven't found a perfect tree yet either.
Any board, beam or post with the pith in it will split or crack.
Wood shrinks as it dries. If you want a particular finished size you have to cut it larger to allow for that shrinkage. On 2X4's and 2x6's I cut 1/8" over size to allow for shrinkage. It's not exact but close. But decide early what size your going to cut and stick with it. That way wood you cut today will match what you cut next year. But if you are cutting somebody else's wood it's their call. Some good calculators here
http://www.woodweb.com/Resources/RSCalculators.html and lots of other info on the site.
Do a web search on Nominal verses Actual sizes for dimension lumber. Hardwood sizes are a whole different book of rules on sizes.
Log diameter is measured on the small end. Big end don't count for "size" and can cause headaches in sawing.
Try and center knots in the board (conifer) for best strength and better chance to dry straight. Trees with big knots makes good posts and fire wood. Knots only have strength in compression not bending or tension. The larger the knots the lower the grade.
Redwood is special. It's been used for everything, but in nominal sizes it's not much for strength. Makes gorgeous tables, mantles and patio furniture. Makes rotten fire wood but don't tell the tourists. It still burns.
Don't try and get every ounce of lumber out of a tree. Campgrounds use lots of fire wood and fire wood pays well.
A sharp blade cuts straight, a dull blade doesn't.
And, listen to the boss and have fun.
