What type decoder do I need for the audio on PBS?
I noticed that you didn't mention what sat receiver you're using. To get the PBS AC3, first of all, the receiver has to have a digital output (ie the coaxial or optical SPDIF connection mentioned above), however the receiver has to also pass AC3 through that output. Most newer receivers do, but some older ones don't, or in some cases don't, until you upgrade the firmware.
Also, some receivers aren't compatable (for some unknown reason) with some decoders. I have 2 Soundblaster Extigy stand-alone sound cards that decode the AC3/DD-5.1 signal, and I had used it for years with 2 Fortec receivers on the PBS channels, however when I got a Fortec Mercury, there was something different about the AC3 signal coming out of the Mercury, such that it wouldn't work with either of my Extigys, whether I used the optical input or if I'd use an optical to coaxial converter in between, and the Mercury's signal also couldn't be played by another decoder I have. I eventually found a cheap home stereo that worked with the Mercury, and also got two of those Sonic Voom things that worked fine until I finally stopped using the darn Mercury because Fortec never corrected any of the multitude of other firmware bugs. However it's always been a curiosity to me of why it's AC3 signal would work with some decoders, but not with other decoders. I've run the signals into an oscilloscope, and I really can't see any significant difference between the signals my Mercury puts out, and the signal my other receivers puts out, but there is obviously a difference.
But back to the receiver, if you have a newer HD capable receiver which has the HDMI connection, and a TV with that input, then there should be no problem. But if you have an older SD sat receiver, then your choices are something like an old Soundblaster Extigy (unless you have a Mercury), the Sonic Voom, a modern audio system with a digital input, or a TV with a digital input. Problem with the TV option though, is that often the TVs might have only one input source that can use this digital input, so if you have multiple sources, you may run out of inputs that can use the digital audio.
Currently I use the Soundblaster with my STB sat receiver, which feeds one of those 4 input RCA switch things before going to my TV, so that frees up the optical input on my TV for other devices. My two HD sat receivers feed my TV via the two HDMI inputs on the TV. I also have a couple PC sat receivers that feed a Roku HD1000 box, which decodes the AC3 to my TV via a digital SPDIF input or via the L/R RCA inputs via stereo downmix.
So there are LOTs of different options..... all depends on what sat receiver you have, what TV you have, and if you're intending to use the surround sound capability through a stereo system with the L/R/C/LR/RR 5 channel system, or just a L/R stereo system.