Now, assuming that I err on the side of too many wires (rather than too few), I think I'm looking at 25 or more wires total. So, Do I need a 25 port router?? Do they even make those? Are they bloody expensive?
I currently have a half-decent gigabit router which I paid $90 for. But it only has 4 ports. Thats obviously not going to cut it.... or is it? what If I connect an 8 port switch to each of those 4 ports? Then I'll have 32 ports to use. But does that make any sense? Wouldnt that force the 8 wires from each switch to be bottlenecked into the single wire linking it to the router? I know for my purposes I probably wouldn't even notice such a bottleneck (in terms of transfer speeds), but I still want to know the 'proper' way to design this network.
Do I just get a router with a ton of ports? Or is there a smarter way to do this by using my current router and a few switches?
You have a few different options. I have a 4 port wireless router that I plug into my cable modem. All the wires in my house terminate in the closet and are clearly labelled. I simply plug the 4 that I am currently using into the router. The upside is it's cheap and takes little space, the downside is you can't use more than 4 at a time and if you change you have to reconnect wires in the closet.
Your other option is to do what your diagram showed. Get a large (32 port) switch that all the rooms plug into, and then connect that to your wireless router or wireless modem. Downside here would be that your switch will be expensive and pretty big.
A compromise is to get a smaller and much cheaper 8 or 16 port switch and just plug in the rooms that you think you will use most often. Most likely you're going to be using a static amount of jacks that won't be changing too often. With an 8 port switch and a 4 port wireless router, you'll have 11 ports (8 +3) that are always connected + wireless.