Remagnetizing a BLDC magnet from a floppy drive
There may be a helpful and useful "instructables" article for you to consider: DIY instructable on making a wind-powered generator. There's also a PDF on making permanent magnet alternators that may be of some help, as well. If all you want to do is to generate on the order of 10W, then the above designs will have to be scaled down. (I'm also somewhat interested in the topic, so I may attempt something like this over the next year.)

The second link above emphasizes my point about using neodymium magnets, saying that these are what makes such a DIY generator within reach of a hobbyist. So it does support my earlier suggestion regarding the type of permanent magnet you should consider using.

For smaller alternators, such as the one you may be considering, the use of the commonly found smaller cylindrical shaped magnets are fine. You should look for the more powerful kinds, such as the N50 type. The higher the number, the stronger. (I think N50 is near the top of affordable magnets and is commonly found on ebay and elsewhere.) These cylindrical magnets are configured (usually) so that one circular face is (N)orth and the other circular face is (S)outh.

The magnets are used to complete two rotors, in between which is sandwiched  a stator (a collection of coils laid out and wired up in a particular way.) The stator stays still and is connected to circuitry. The paired rotors within which the stator is sandwiched, rotate with the applied mechanical rotation mechanism (hand crank, etc.) The stator material holding the coils should not interfere with the magnetic fields, so a resin of some kind is often used for this, letting it harden with the coils embedded in it. The rotors are usually a circular plate of iron or steel (necessary) and you will want to place the cylindrical magnets so that they alternate the polarity of the face against the plate as they are added evenly around the rotor plate. (An even number of them.) The steel or iron in the plate forms an easy pathway for the magnetic flux. The magnets around the rotor will then have only one exposed face to rotate near the coils in the stator.

A common DIY arrangement makes the stator diameter larger than the rotor diameter, so that the outside perimeter of the stator can be bolted to a fixed block. The stator has a hole in the center so that an axle may connect the two rotors on either side and spin freely. The inner faces of the rotors and both faces of the stator need to be very flat and arranged as close to each other as practical. Shoot for \$\frac{3}{32}\$" but it's probably asking too much to get closer than \$\frac{1}{16}\$".

Complete details would be hard to include here in a long-term stable form, but here's another page where you can see how things might be assembled together: alternator assembly.

You will also need to find or design a controller for your purposes. But I'd recommend concentrating on completing a working alternator first and then purchasing the controller for your first attempt.

Best wishes!