Welcome to the forum, Brandon! Very cool that you included photos of all of the connections.
I don't agree that you need to buy a new receiver, or that you would ever use the analog connections. There are two fairly easy ways to connect this up:
1. My recommendation is to connect the PS3 to the TV using HDMI, connect the PS3 to the receiver using the optical audio output, and then go into the PS3 audio menu and set it up to output audio over the optical output. This will allow you to get 5.1 audio from the PS3
2. Alternatively, you can connect the PS3 to the TV using HDMI, set up the PS3 audio menu to output audio over HDMI (probably the default), and connect the TV's optical audio output to the receiver. I didn't specifically research your new Samsung, but my guess is that you'd only get stereo sound because most TVs will convert audio from an HDMI input into stereo for output through that optical audio output (but, you can always try it)
The advantage of an HDMI receiver would be the ability to get 7.1 audio from blu-rays, but that would only matter if you have a 7.1 system set up and the blu-ray actually has a 7.1 audio track (a lot of them don't).