Verizon DSL modem and Linksys routers coexist just fine.
I don't recall all the details, but here are few pieces I recall from my old setup as well as one I did recently for someone.
Shut off the computer. Then the router (pull the plug), then the Verizon modem (has a switch, right?).
Connect computer back to the DSL modem and tell it to be just a router, not a DNS server, nothing -- here's where I don't recall the details unfortunately and that's the most important part. Muddle your way through somehow, please.
Then turn off the computer. Turn off the DSL modem.
Replug Router into the modem, and computer into the router.
Slowly turn on DSL modem, wait till it stabilizes.
Turn on the router, wait till it stabilizes.
Turn on the computer.
Tell Windows to use 192.168.1.1, obtain IP address automatically, ditto DNS and DHCP if I recall.
Run IE. In the address bar type 192.168.1.1 and setup PPPoE, enter username for Verizon - that funny name they gave you - and enter password.
Almost immediately the router fills in the 2 DNS server Verizon uses and it's good going from there.
Sorry I don't recall all the details, but the important part really is what the DSL box does. It has to be made into just the translator, and Linksys will do all the serious work since it has a great firewall.
usasma, it's funny how different people like different things

Verizon gave me a DLINK router or FIOS, free. I couldn't stand their ugly and confusing interface, couldn't stand one IP address merging with another ... ended up trashing it and back to Linksys

That was couple months ago, which is why I can't remember my old setup too well. If help still needed here, I'll dig out some old notes.