........ I would rather just buy a new phone and stay on my old everything plan. Is this possible ....
As Caesars indicated, if you buy a new phone at retail (or from someone else via Swappa, Craig's List, etc.) and put it on your line, you can keep your current plan.
However, I would like to complicate your decision. Do the math. Do you use enough data to justify paying more than you might under the new Share Everything Plan? You realize that the subsidy you get for a new, top of the line smartphone is about $400 off retail, and given that you can upgrade every 20 months, that amounts to about $20 per month that you give up in order to keep your current plan. When you analyse your data usage, keep in mind that because 4G is faster, you may tend to use more data than when you had 3G.
To further complicate the issue, T-Mobile has announced that in 2013, they will discontinue subsidizing phones, and customers must buy them outright, pay them off in monthly installments, or bring their own. Will Verizon follow suit? Will this go-round be your last chance to get a subsidized phone and from then on out will you have to buy your phone outright? Will the change to non-subsidized phones (by VZW), and hopefully lowering of the plan rates, be the final blow to those who are hanging on to Unlimited Data, making the cost to retain UL very expensive?
I'm looking at this issue from a low end data user. In my case, I can't justify hanging on to UL at any cost. For a heavy data user, it may be prudent to hold on to UL and forgo what might be the last subsidy available.