Good question. I have some pointers for you!
1) For small items, try this (or mirror image obviously!) set up on a cloudy day/8am/4pm - aka not bright sunlight 0 your apartment actually sounds perfect for this!:
The idea is to not have too much direct light from behind your camera on your piece, this "flattens" the item - due to a lack of natural shadow. The backing boards can be as simple as white cardboard painted white, or covered in white/cream (cream is my preference) paper. I have a big A3 sheet that comes down and becomes the 'floor' too:
The main point of the extra (unseen) backing board is to reflect natural light back at the piece from the other direction, instead of this light getting lost in the room. Have a go with and without the board and you'll see a huge difference in the shadows, they soften and it makes the camera's job a lot easier - it's no longer focusing it's contrast based on shadows, but instead on your item itself.
Here's an example of a photo I took when I had just started using this method.
2) If you have any preset "scene" options on your camera, and you want to use a white background, try out "Snow" or "Winter" - it works amazingly well to combat the problems you experience with white backgrounds
3) Try getting the floor to be white - you can see the difference the floor is making in your own photos! I think because the camera thinks the floor is the darkest point, and other colours can get washed out in comparison. Or in your case it could be that your shiny floor is reflecting too much light back at the camera, and it's underexposing to adjust for this! To do this, get models to pose on a double sheet which you've hung from the ceiling (or above your photo height) and covers the portion of the floor which will be photographed.
Good luck - I'd love to see some photos after you've given some of my ideas a go!