As stated already it will depend on your budget, but it also depends on what type of shooting you are doing, skill level, if you are looking for something compact.
1. Canon S110: I have been using the S100 for a few years which is almost the same, you can take quality photos with this camera and even great macro shots without any close up lens ( a close up will improve the shots even further). I primarily use this camera when I am a guide as my G16 can be a bit much to take down with me. The S series can also take great shots with just the built in flash and housing diffuser. I use the Ikleite housing but have used friends Fix housing a few times and prefer that more as you can use the rear function ring but it is a bit more costly. I have used strobes with the s100 before but again I mostly use it for when I have customers. The S110 will also be compact compared to the G16. This camera is great from beginners in my opinion as it can be used fpr Auto and gives you the capability to use manual, AV, or TV and still get some great shots. The wide angle is not so wide and would require the use of a wetblens for best wide angle shots. For low light the camera has a harder time focusing if you do not have a focus light. I would stay away from the Canon housing is possible, same features as the Iklelite but the Iklelite housing is more durable.
The G16 is a great camera for those who want more from a "point and shoot" as it gives you more performance when shooting in Manual, AV, or TV, you will also beable to take better wide angle and macro shots where as the S110 will likit your wide angle without any wet lenses. The G16 will give you some amazing macro shots as you can get quite close without any close up lenses. The camera wprks very well in low light situations. The G16 also takes some great video underwater amd you can also whote balance the videos quite well. Housing of choice is the Nauticam aluminum housing but is a bit $$$, next would be the Fantasea as it is a good quality poly housing and is quite reasonable about the same as the Canon Housing again I am not a fan of Canons housings, I would not recomend Iklite for the G16 as it is basically a big box and I never found it very comfortable when I had one for my G12, the Recsea housing is not bad but innorder to attach a dome you need to remove the standard port and install the dome port, with nauticam or fantasea you just have to purchase adapters to mount the domes and many choices of wet lenses. Next you can add a whole lot of features strobes, focus lights, wet lenses and create a great kit. The G series line has always been popular for underwater photography and great for the compact size. The G Series can be used as a beginner who has the willing to learn look theough the forums and try to find another experienced diver with the G Series or even SLR experience to help you produce betetr photos. With this camera you can expand a bit more as where the S series you will not necesarily be limited but you will find yourself wanting to upgrade and it maybe sooner than you think.
As for the RX100 I do not have any personal experience with this camera but I have seen some colleagues take some amazing shots with it, and it is also a nice compact camera compared to the G16. Since I do not have first hand experience with this camera I will not comment any further as not to misguide you.
I would suggest taking a quick look at the cost of camera + compatible housing then set a budget. Select your housing carefully as it can be easy to outgrow in the future. There is another brand of housings that looks similar to Canons STAY AWAY I have used them and had nothing but issues as well as other divers Ive known, they are basically a bad knock off from China for about the same cost as the OEM.
Here are photos from earlier this year on a trip in Myanmar, Canon S100 ikelite housing, no wet lens, no strobe built in flash only, unfortunately I was not able to use my strobe and lenses. I don not have my G16 shots up yet as I still have to await approvals to publicly post them :/
https://www.facebook.com/media/set/?set=a.1496976280519888.1073741848.1493861857497997&type=3
