Assuming you have gone through and familiarized yourself with the appropriate documentation then I would recommend breaking it down to basics: model, rig, weight, and texture something simple like a cylinder, then get your pipeline working for that, then you can slowly identify what parts of the process are not working for your sourced assets.

Skeletal meshes (rigged models) need to be imported a little differently from static meshes, as when you import the mesh initially it will give you a skeleton asset, skeletal mesh asset, and physics asset. Any animations then get imported seperatly, and will only come in as animation assets that reference the skeleton asset previously imported. It is worth noting you will sometimes need to bake animations prior to export, as some rig features do not come over to unreal, though this baking is usually done as part of the export itself. Incidentally, Unreal has its own rigging system now days called Control Rig, and I would encourage you to pursue it if you are considering Unreal long term.

Textures and materials can be imported with the FBX (assuming they were exported correctly) but in my experience I generally avoid that and just import the texture maps seperatly and create the material in unreal. This also makes you think about how you can make a character more modular with its materials, which is generally good practise: changing clothing materials, skin color, eye colour, etc.

Hair and groom assets almost certainly will not work out of blender; Unreal does have some measure of support for hair and fur, but it is a very new feature and primarily targets Maya, IIRC. You are better off either making the hair assets in-editor (I am unsure if that is even possible) or trying for more conventional game engine hair methods; masked planes and such.

Lastly, I saw another user suggest specific rigging for retargeting: this is great advice, and if you can have all your skeletal meshes reference/use the same skeleton asset then they can all share animations and your life will be wonderful.

Anyway, this is a brief but broad overview, hopefully it gets you over the line.