You can still get a 2 year contract. If you are currently in a contract, you can switch to More Everything, and your only choice is to stay on contract. Edge will only come in to play when your contract is completed and you need a new phone. Verizon is phasing out contracts, but as of now, you will get a choice of Edge - now called device payment plan, or traditional contract. Some are offered Early Edge, which is early upgrade, but generally this is a bad deal for you and has caused lots of angst among users.
When it is time for a new phone, don't automatically choose contract. Price out the 2 year costs each option will give you and choose the cheapest. It is very often that the device payment plan option ends up being cheaper, sometimes by a couple hundred dollars.
If I switch to the MORE Everything Plan do I have to start using Verizon Edge? No. Or can I stick to my 2 year contract plan? Yes, your contract will not change, just the plan you are on. In many cases, More Everything is a much better deal than the old Nationwide plans.
Also just wanted to verify that you get unlimited talk and text with the More Everything Plan. Yes, unlimited minutes and texting for all lines, and a data bucket that is shared by all lines on the plan. And a discount on the access fee for each line as the contract expires - that's where the real savings is if your lines are out of contract.