Just to have this on a place where I can find it easy ;)
Shortly, is this:
The way to calculate that is 60,000 / Tempo (in BPM) = one quarter note, in milliseconds. So at 120 BPM, 60,000 divided by 120 = 500 ms. Divide that in half for an eighth (250 ms), and that in half again (125 ms) for a sixteenth note.
More complex is like this:
First of all, what is "pre-delay"? Basically it's just a short delay time before the onset of the reverb. Imagine you're standing in the middle of a hypothetical 100' X 100' X 50' (ceiling height) concrete room. If you were to light off a large firecracker, the sound from the explosion would radiate out in all directions at the speed of sound - about 1,130 feet per second. That translates to a distance of 1.13 feet per millisecond. It would take approximately 44.25 ms for the sound to propagate outward from the source of the explosion before it came into contact with a reflective surface (not counting the floor). Once it hits one of the room boundaries, it bounces off - reflects - and continues to travel in new directions. These initial sound reflections are called "early reflections", and are a big part of how our ears determine the "size" of a space. Once the echoes become so widespread and diffuse that we can no longer distinguish them as individual echoes, it's reverberation. The length of the reverberation depends on many factors, such as the room or enclosed space's construction, dimensional ratios, size and contents. The length of the reverberation is normally indicated by its RT60 time, which is the length of time it takes for the reverb to drop 60 dB from the level of the original source sound.
Now if you're looking to nail the sound of a reverb, you should look at the way the "real" room or device works for some clues as to how to set the parameters of your reverb device.
For example, a spring reverb doesn't have the "wait time" - sound is being generated by an electronic driver circuit hitting one end of a (usually) 9" - 18" spring or three, and the vibrations of the springs are picked up at the other end and sent to the output. There's very little (if any) real pre-delay - maybe a few ms max. There is usually little in the way of early reflections and the decay time is usually not overly long.
Let's look at some of your other options:
Plate. A plate is another mechanical reverb, and it functions similarly to a spring reverb, but instead of a few short springs, a plate uses a large sheet of steel that vibrates. The sound is normally fairly bright, and less "boing-ey" than a spring, but still somewhat "metallic". If your plate reverb doesn't have a pre-delay feature, you can simulate one by putting a delay unit in series before the plate in the chain. You could do that with a spring verb too, but in my experience, that's less commonly done. IOW, I don't normally look to any rules as far as pre-delay on a plate, and would adjust the pre-delay time to a musically useful value. By that I mean setting the time so that it's long enough to give a bit of space between the source sound and the onset of reverberation. Doing that with any reverb can give increased intelligibility to the sound source, but if you set it too long, it starts to sound "un-natural", and it can cause intelligibility problems with following notes.
Room reverbs are something you should be fairly familiar with from "nature". There's a huge variety of different rooms, so like all these terms, it's really a quite generic. In general, a room reverb would normally have modest to fairly heavy early reflections, but they'd be quick (short) and the onset of reverb would be fairly fast, although the decay time is going to depend largely on the size of the room and what is inside it. A small, heavily and "softly" furnished carpeted bedroom is going to have a very short RT60 time and lower amplitude early reflections vs a large , sparsely furnished, brick-walled and wood-floored living room.
For even larger "rooms", such as chambers (even an "elongated space like a stairwell" - the dimensional ratios are what matter more so than the way a room is oriented) and halls, you can extrapolate from there. The larger the space, the longer the pre-delay. Halls traditionally are sized and shaped and decorated in such a way as to provide reasonably long and diffusive reverberation. The size of the hall you're trying to simulate should determine your pre-delay time. I'd start with maybe 40 - 60 ms and experiment from there, going longer for larger halls. Chambers can be anything from your stairwell (and I love the sound of a good concrete stairwell) to underground parking garages and even purpose-built recording studio reverberation chambers. They tend to be made out of concrete, are fairly empty and very reflective and "live" sounding. RT60 times can run fairly long (several seconds for very large chambers), and early reflections are well represented. Your pre-delay is going to depend on the size of the space you're trying to simulate, and again, I like to dial that in so that it makes musical sense rather than getting to slavish in trying to simulate a precise chamber "size".
Caves are very reflective environments, and irregularly shaped and usually fairly diffuse sounding. Large caves with the right dimensions and multiple adjoining caverns and passageways can have incredibly long and heavy reverberation, and this is what most "cave" settings seek to emulate, and it's is the one to reach for when you're looking for an "over the top" style reverb sound. The sky's the limit on max reverb pre-delay times here, although if you're going for the sound of a smaller cave instead of a large cavern, or the sound of a man-made "cave" such as a mine shaft, you might want to go a lot shorter on the pre-delay time.
Tile? My assumption is that they're trying to simulate the sound of a small tiled room such as a kitchen or bathroom, although it could be a larger space such as a locker room. In such spaces you'd have very heavy early reflections, and they'd be pretty fast and may ring out for a while due to the highly reflective room surfaces, but because of the relatively small space, you're likely to have a high ratio of reflections to true "reverberation". Even the high frequencies will bounce around a lot in a tiled room because there's little there to absorb them (highs tend to get soaked up by things like human bodies, room furnishings and carpeting fairly quickly - usually much easier than bass frequencies), so the character of a "tiled room reverb" will usually be fairly bright.