The solution I found:
In ALBUM VIEW: if you click the "play" triangle icon that pops up over the artwork you will get the whole album to play in order (no shuffle); If you click the "play" icon in front of a song, it shuffles after that song; if you double click the song, it will play the album in order from that song to the end of the album. If you WANT to turn shuffle on after starting from one of the "non-shuffle" modes, click the shuffle icon in the upper center display.
In SONG VIEW: you can only start a song by double clicking, so it will play in the order that is listed (e.g. album by artist by year or alphabetically, etc). If you WANT to turn shuffle on click the shuffle icon in the upper center display.
In ARTIST VIEW: similar to ALBUM view, but it doesn't shuffle when you click the "play" icon in front of the song. Also, if you click the "play" icon of a song, it will play that song, then finish the album you are in and then go on to all the other albums for that artist in order. If you click the "play" icon over the album artwork it will only play the album you clicked on.
Unfortunately, none of this is intuitive, and I've noticed there are slight changes that occur depending on what you do first (for example, once I got shuffle to turn off, it wasn't automatically starting again when I clicked the "play" icon in front of a song).
I don't understand why Apple feels some demented need to constantly tweak iTunes with things that nobody gives a **** about (and which actually, judging by this thread, really irritate most users) and yet, they STILL won't ALLOW us to input or change the freakin' release date of a song. iTunes doesn't even use this field, and when they do they are usually putting in inaccurate and incomplete data. The "fix" is a ridiculously time consuming work around too (if you don't know about this "fix" you just change the media type from "music" to "book" and then you can put in a release date and when you switch it back to "music" it will keep the date).