What are the SOFTEST breast implants available?

Good question. Much of the final look and feel achieved after breast augmentation surgery depends on several factors:
1. The initial shape, size (volume of breast tissue), symmetry of the patient's breasts. In general, the better the preoperative breast appearance the more likely the breast augmentation “look” will be optimal. 
2. The experience/skill level of the surgeon is important in determining the final outcome. For example, the accurate and gentle dissection of the breast implant pockets are critical in producing long-term well-placed breast implants. I personally think that these 2 factors are more important than any others, including type (saline or silicone) or model (low/moderate/high profile) of implant.
3. The type of implant used may determine the final outcome, especially if the patient does not have significant covering breast or adipose tissue. For example, some surgeons feel that silicone implants have a more natural look and feel than saline implants because silicone gel has a texture that is similar to breast tissue. In other words, if a patient has very low body fat and/or very little breast tissue, the silicone gel implants may provide a more "natural" result. All FDA approved breast implants utilized today are cohesive gel silicone breast implants;  some are firmer than others (including the true "gummy bear" breast implants).  I find that I use round smooth silicone gel breast implants for the vast majority of patients who seek breast augmentation surgery.
4. The size and model of breast implant used may make a significant difference in the final outcome. Therefore, it is very important to communicate your size goals with your surgeon. In my practice, the use of photographs of “goal” pictures (and breasts that are too big or too small) is very helpful. I have found that the use of words such as “natural” or “C or D cup” etc
Also, as you know, cup size varies depending on who makes the bra; therefore, discussing desired cup size may also be inaccurate.
  To summarize: select your plastic surgeon carefully. Communicate your goals carefully as well.  Chances are you will be very pleased with the outcome of breast augmentation surgery. 
I hope this helps. Best wishes. 

If you desire softer implants, silicone feels softer than saline.   In the silicone line, the smooth round implants feel softer than textured round implants.   The anatomical or teardrop implants, high viscosity gel and " gummy bear " implants are much firmer.   So smooth round silicone implants are probably your best bet.