Here's a rundown of how I typically lay out my fortresses:
Strike the Earth and channel down at least three Z levels, via a three-tile-wide slope which allows trading caravans access to the main entry hallway. Three levels down clears you of all common surface water issues, you'll never hit "damp stone" digging if you're that far below the ponds and rivers. Farms usually go one Z level above the main entry (2 down from the surface), and they need to be dug carefully to avoid damp stone underneath the surface water. The entry hallway has space for a trade depot branching off to the side, and further down the hall we get to the main fortress staircase. Entry-Z-level stuff includes the main stockpile and main early-game workshops. the staircase goes down into the depths from here (and perhaps 1 Z level up for farm access).
The above gives you a long, wagon-accessible main entry hallway which can be secured via bridges if that's your desire, it protects trading caravans from surface threats, and allows you to control the flow of your visitors and traders to allow for both accessibility and security.
From there I dig down until I hit the caverns. Sometimes it's 60 Z levels or more away, but I keep digging down until I determine where, at the very least, the first cavern layer is. This gives you the data you need to set up the multi-Z-level features you're talking about. Sometimes cavern 1 is close to the surface and you need to keep digging down until you hit caverns 2 and 3, just to find space for those larger features.
Once you've got the Z-level data, understanding where things are clear and where they're occluded by caverns / magma / etc, you can plan out everything else accordingly.
Typically I will divide my waterworks into low-pressure circuits and high-pressure circuits. The low-pressure stuff will be the tavern waterfall, any drinking water supply, the hospital water supply, etc. The high-pressure stuff is typically used for fluid logic (high pressure makes the logic operate more quickly). Sometimes I use the high-pressure circuit to deliver water for low-pressure uses, but in that case care needs to be taken to include, as you reference, diagonals for pressure control.
Any major water use area typically has one "empty" layer above and one below it, which I then use for supply plumbing and drains respectively.
The source is usually a surface river, which I tap into an underground channel system. I always put a lever-controller bridge at the very top, which is my master shutoff valve. This typically splits into the low-pressure circuits which are directly fed by the river, and a drop to a very large multi-Z-level reservoir (the "high pressure reservoir"), which then feeds a small dug-out "high pressure junction" which has individual feeds for all the various high-pressure delivery needs. I always dig out more unconnected feeds than I need, so I can add destinations to the high-pressure circuit easily without needing to drain the entire reservoir.
The drains are typically located at the very bottom of the fort - not always, but most of the time. All the various individual drain locations merge into one large drain reservoir at the bottom, which frequently drains off into the third cavern layer off-map, or if I'm feeling really adventurous I'll try to get it to drain into the HFS. For security, I'll often set up an automated fluid-logic-based auto-drain, which automatically opens a lower bridge when the reservoir hits a certain level, draining the whole thing in one wild high-pressure blast, subsequently closing the lower bridge until the next time the reservoir fills. This is fairly easily accomplished via water-sensitive pressure plates and a little fluid logic.
If you're making something large or complicated it really helps to keep a written reference to the fort's Z levels. My most recent still-ongoing megaproject fort is actively using nearly 100 Z levels for various purposes, all carefully positioned as there are a lot of moving parts to keep connected and choreographed. The most important thing is really to locate the cavern layers, as they will determine a lot just by their positions, and then place the large things first, trying to leave yourself room to fill the smaller stuff in around them.