There will always be a fully visible background when you just play/ view footage in your bog standard media player. Transparency handling is entirely a matter of specific editing/ compositing tools or specialized playback software/ devices actually interpreting that info and that's the part that you and your client need to understand. Unless they use such tools, all the transparency you create doesn't do them any good when they feed their monitors from a standard PC playing a clip in fullscreen. Likewise they will have to get used to that they can't have both - compressed formats like any MPEG or WMV do not support transparency. Their whole point is to balance data rates and best possible playback speed. So again, your client will have to use suitable software or hardware to create those playback clips in the first place based on your intermediates with the transparency.
If a media player is used to play back a clip with a transparent background the background will be black because Media Players (Quicktime and Windows Media) do not support transparency.
If your final product is for flash then you need to export an FLV with transparency. If your video is going to be played with an HTML 5 player then you have to match the background color of the video to the background color of the page where the video is being played. If your client asked for one of the four formats you listed and wants a transparent background then the client must be educated so they understand what they need and what they should be asking for. The only format listed that supports transparency is H.164.
Without more details about your project this is about all I can give you at this time.
Here are some links that will teach you a bit about HTML 5 playback with transparency.
More information: the client asked me to make several 15 second animations that they will play on a 'clever display'. Those displays can only handle the 4 formats I mentioned. They want to be able to switch the order and duration and leave some white space in-between them. But even though I use a white background (#FFFFFF) you can still see the transition from the (background of the) animation to the white background of the clever display. Supplying the animations without a background would solve that problem.
Will I actually be able to render the animations in a format that supports transparency (like quicktime animation, if I'm not mistaken) and then use en encoder to get it in H.164? And even if that works, the clever screens wouldn't automatically accept it?
Is this the what you mean by clever display? http://www.cleverdisplay.com
If this is the platform your client wants you to deliver to then contact them for advice and techniques. Exactly matching their background is a matter of color management. There is no technical information on their site about creating content for their system so the only way to know if their player supports transparency is to talk to them and get the procedure. That's what their customer support department is supposed to do.
This is exactly like creating content for broadcast on the major networks or cable systems. While it is a lot simpler than it used to be, you must ask for specifications before you deliver product to them or your work may be rejected as not suitable for broadcast. Not asking is the sign of an amateur. I've been producing product for film and TV for more than 40 years and I still ask for specifications every time, not from the client, but from the folks that will be using the content in the long run.
Once you know if their player will support transparency, if you can't figure out how to encode encode it. I was a little inaccurate when I said that h.264 supports transparency because, as far as I know, there is no current commercial encoder that will render a true 32bit h.264 file. Here's an article: iOS Graphics and H.264 with Alpha technique. It's not going to be as easy as adding your comp to AME and choosing h.264 / 32bit... RGBA, because you can't to that.
Sample setup for exporting from AME with an alpha channel: