Continuous can be easier to start with as you don't have any issues with triggering and syncing, and you get instant feedback as you can see the effect of the light as you move it. Strobes have the advantage of being able to overpower your ambient light so you don't have to work in the dark. They also don't get as hot as they are only on momentarily.

You only need one light for the subject, you want a soft slightly directional light, so a shoot through umbrella would be best. Two lights for the back ground make it much easier to get an even light as you want it white everywhere, not grey toward the edges. You can get away with one light however, especially if you place it behind your mannequin. Background lights should be hard (no light modifiers).

With only 4x5 meters of space to work with your set up will be very compromised. You wont be able to get your background to go to pure white everywhere without some of that light reflecting back only your subject and giving it glowing edges, so do the best you can but you're probably going to have to do a lot of work refining the edges in Photoshop. It's still work trying to light in layers.

Given that your budget has to include lights and triggers I would start with a 2 light setup (you can always add more). See this question for info on getting a white background with only 2 lights:

How can I inexpensively create the white backdrop look?