There are a few different options for video calling. i do not know how many of them will support the options you want, but i will try to specify their uses as best i can.
The new version of Google Talk
It supports video calling and handles it well. You have to call from within the app though, i don't believe there is built in platform support for calling from call logs.
This is a widely used, multi-platform video chat app that has many options, and i know it allows you to remove your self image, group chat, and it pulls from your contact list to give you a list of other Fring users. On occasion, it has worked with Skype (mobile-to-desktop), but in my experience, this has been spotty.
The advantage to Qik is it's incredible online support. It has been improved greatly since it's introduction to the mobile market.
This got the last spot because it is personally my least favorite. You can only call to other devices using Tango, which i find extremely limiting, but it is the same scenario for Qik, so it'll have to be dealt with. It has very positive reactions from users though, so it's worth a look.
i hope this helps you get a jump start on finding a solution to what you want. Take a test run with one or a few of these and let us know what works best for you!