Your Sigma 70-300 will probably be fine for the shots, it doesn't need to be that fast as i doubt you'd be using a very fast aperture... Stick it on a tripod as well to make it easier for yourself, but have it slighly loose so you can swivel it around a bit to recompose.
As mentioned above if you can use your flash off-camera then that would be the most effective and of course diffused in one way or another...
Make sure you're not shooting too close to a background, and at some points you may want to light up the background so if have a second flash then that would be ideal.
Some shots you may want to also include a hairstyle so another light for hair would be necessary (but then you wouldn't need to light the background - so two lights should do overall).
I'd also recommend a silver/gold reflector to help place the light more.