I prefer using lenses in the Normal range of 35-50mm (35mm film equivalent) for newborn sessions as I shoot most of them on site and often in cramped settings. I queried the past year of newborn shoots and had the following distribution of lenses to images on a full frame camera:
It's worth noting that for portraits many people will stay clear away from focal lengths this wide. I agree for weddings and similar situations that anything wider than about 50mm should be avoided in most situations. Out of necessity due to most on site shooting locations I've found that 35mm often works very well for me. Also, newborns are quite forgiving!
On an APS-C sensor I would be completely comfortable shooting an entire newborn session with either a 24mm or a 35mm lens. On a full frame sensor I would feel the same way with either a 50mm or a 85mm lens.
Recently I personally have moved away from 85mm lenses as I just want to carry around less gear but the 85mm f/1.8 is a great option for newborn photography especially on a full frame sensor. If you know you will have more room, a 85mm on an APS-C sensor will certainly get most of the shots for a newborn session. I have used a 135mm lens on more than one occasion when I have the room and want the look a longer length can provide. But the vast majority of the time I don't have room for that focal length especially if I were using a crop sensor.
Beyond the most standard angles, macro shots are often nice to emphasize the small nature of babies. This may not be something you buy right away but you could look into cheaper alternatives such as extension tubes (although I find them quite difficult to use with a newborn).
An additional consideration would be if you want any overhead shots. If you want to capture from above the subject you either will need a wider focal length than 85mm or a tall stool to stand on(be careful!). An example of an overhead shot that is much easier with a 35mm(35mm eqiv) focal length:
You have a pretty limited kit, but in most cases you don't need a ton to do a good job with newborn photography.
Typically I would recommend having 2-3 off camera flashes in case the room has few natural lighting options. It also can just help you control the scene instead of leaving it up to the clients home and the weather conditions that day.
Other equipment you may want to strongly consider would be props. Items like wraps to me are critical, and other gender specific items can be nice as not all clients will have options provided. Beyond clothing; backdrops, flooring, baskets, etc. can all be very useful and add a lot to the image. It really comes down to what type of images you are trying to create. I personally try to strike a balance between elegant/simplified imagery and over the top setups which can require a lot of unique pieces.
Finally, although your question is equipment based I feel the need to bring up the most important concern of newborn photography and that is safety. I won't get into all of the details but since you are new to this you really need to look further into it. At a minimum always keep the babies safety at the top of your mind and don't try to recreate an image that may put the infant in any danger.
- A normal focal length lens between 35-50mm (35mm film equiv) with an aperture of f/2 or greater
- A large diffused light source
- Outfits, blankets, backgrounds, wraps, props, etc.
Nice To Have
- Beginner set of 2-3 off-camera light sources with softboxes or umbrellas
- Portable backdrop system and backdrops
- Portable heater
- Macro lens
- Neutral density filter (to allow for wider apertures and flash)
Make sure to check out the baby-photos tag at this site for lots more info on this topic.