There are multiple versions of Tomato now, base/original and others mostly featuring support for USB, VPN, Optware etc... Unless you're looking for some specific feature from those others though it's best to stick with the base version when you're starting out.
Biggest advantage for most people is the better implementation of port forwarding and NAT-PMP/UPNP for torrents and games. Memory management is also much better with reboot being few and far between. Logging is also available which helps with troubleshooting when you can see exactly what services are or are not working as well bandwidth control. Other things like static internal ip address assignment come in handy even on a home network. There's a lot to list but anything that can use DD-WRT or Tomato is usually better off for it.
I find Tomato to have a better UI and upnp setup than DD-WRT but that's a user by user thing.
Also it's probably easiest to install DD-WRT first and follow whatever instructions they have for your model. You should be able to do all of it over the web interface alone. Haven't looked into the 160N so there might be a gotcha *but* if there is, DD-WRT's router database will have a wiki article with step-by-step instructions. Afterwards you can use the firmware update page to just flash whatever else you want.
It's pretty difficult to brick a router, just try it out!
Edit:
Here is your starting point.
Yours is a 4MB model so you'll need to stick to the slightly-stripped variants. Nothing you'd miss unless you're set on running a VPN client/server or something like that. Compatible firmware versions are listed on the dd-wrt router database.