I've been using Linux for 15 years in both business and personal use. I currently use it exclusively on my personal systems. No Windows anywhere. Here are the answers you need:
1. Linux installs on nearly all modern PC hardware. Unless you have something peculiar or really exotic, it should work. When you install one of the current distros, the detection will take place and if there are issues, you should know then.
2. Linux doesn't care about routers and modems. If you connect to the router for internet access, it's the wireless or Ethernet device on your systems that matter. Again, networking with Linux works out-of-the-box in nearly all cases. If the router and modem speak Wireless or Ethernet, it will likely work fine.
3. There are a lot of great distros for first-timers. I would look at PCLinuxOS and Linux Mint. I don't use them myself (I use Slackware, which is NOT for beginners), but I have seen them work, and they are terrific for ease of installation and use.
4. Deal with BSD later. Linux has far more support and available software.
Check out the Linux distro site for details on all Linux distros:
http://www.distrowatch.com
Each distro has plenty of support websites, and most are listed on the Distrowatch site.
I want to comment on a couple of things the guy above me (Michael) said.
1. Very few of the modern distros use LILO anymore. In fact, I can only think of one (Slackware), and you have the option not to install it. Most use GRUB to load, and most detect the current drive settings and add any Windows partitions you have to boot from so you can dual boot your computer to either system.
2. Linux installers do not do anything to the BIOS and nothing to the drives unless you direct it to in the installation. I have no idea where he gets that from. A Linux installation is very similar (in fact, easier) than a Windows install. You select or create a partition and install it. It doesn't touch anything unless you tell it to do so. Yes, you can do an automatic installation, but that's also a choice.
3. Just because someone is a second-level tech support at Dell doesn't mean they know anything about Linux. Stick with the sites dedicated to your distro and with Linux in general. You will always find a solution to any problem and all the help you need.