To add to Steve's excellent advice...
Yes, you need both a computer and a router to make the remote use work. That's how you connect the iPads and other smart devices. The early SLs had no Ethernet port. The newer AI models do.
Macs work fine, newer ones don't have the Firewire port (friggin' WHAT is going on with dropping the ports, Apple??). I"m using my 4-year-old 17" MacBook Pro that still runs like a champ. I've no plans to upgrade anytime soon as they don't make the 17" model anymore.
Mac or PCs is irrelevant, both work fine.
As for routers, if you can make a Linksys WRT54G work, that's fine. I have run into crowded wifi space (as in give a command on the iPad and 4, 5, or even 6 seconds later, the command is executed. For they reason, I went with a gigabit router that would do 5gHz, which is a little less crowded, at least for the time being. I use Netgear R6300 router, which is close to $200. My next one will be around $600, just because I still use one for pro sound work occasionally and I want a really beefy mother. You may not need that robust a router. ASs long as you can make a solid connection and it works promptly, most any router will do.
If you haven't looked on YouTube, there's a to of good stuff and tutorials there.