I'm preparing to do the same thing... in my case I'm using an HDMI over Cat5 extender, kinda like that box you linked. I picked up a receiver that does the HDMI switching, so I'll only need a single HDMI connection from my receiver back to the TV, which will go through that box and run over Cat5. The box I'm using also handles the IR Repeater function for me.
You might find that going from using and not using the receiver is a pain; built-in speakers on flat panels absolutely suck, and in order to simplify remote use, it's far easier to set the remote to control the receiver volume and use it 100% of the time. To go back in forth you'll either have to toggle settings on the TV or fumble with multiple remotes.
As far as HDMI distance, there's no set limit; it depends on the quality and gauge of cable you use; they also make active HDMI repeaters that can come into play - the good cables tend to max out around 40ft... but if you're using the HDBaseT box, does it matter? Where does that thing come into play? Also I'd be wary of that particular extender - it's pretty pricey and says it supports high def, but the specs say it has a limit of 1280x1020 (1080p is 1920x1080). Many people use the term HDBaseT for things that are just generic extenders not using that chipset.
Last, for splitting the output of the cable box, you can either use a splitter, or often the cable box will also have separate audio outs you could run to the stereo. When using a splitter, some nuances come up - if it's a cheaper one, whichever device is on first will do the negotiation and set resolution; when the 2nd is switched on, if it doesn't support the same, it won't get the signal.
You might consider what I'm doing - that way I'll run speaker wire to the soundbar and a single Cat 5 (two in your case to hook the TV up too) and that's it. But also run some form of conduit from the TV to the attic or equipment location so you can handle changing technology.
