Help with first visit to Italy

First, congrats on planning your trip!

I've found the rates flying from NJ very good flying into Milan (which is a lovely city by the way).

Try out your options flying into Milan and out of Rome. I do think starting a journey in Italy from North going South works quite well for most people. Milan is an easy train connection to both Venice and Florence.

You could visit Milan, Venice, Florence, Amalfi Coast and then Rome - in that order
OR
You could visit Milan, Venice, Florence, Rome, Amalfi Coast and fly home from Naples. This would avoid any unnecessary backtracking, but I'm not sure if flights from Naples are more/less expensive to return to NJ so weigh out the convenience/vs price.

Milan deserves 1 day and is a good place to recover from jet lag. If you prefer you can take a train the same day to Venice or Florence.
Allow a 1/2 day for any day you are changing cities.
Venice needs at least 3 days to see properly
Half day for changing cities
Florence allow at least 3 days
Montepulciano is pretty remote and you will definitely need a car if you want to explore efficiently. How many days?
Half day for changing cities
Rome - there is much to see/do here so I'd say allow 4 days
Half day changing cities
Amalfi Coast - easily takes 4- 5 days depending on what you want to see.

If my math is right - that is a total of 18+ days...not counting any days that will be spent at the wedding. So you see where I'm headed with this right? You may want to eliminate the Amalfi Coast for this trip and just stick to the Venice,Florence,Tuscany, Rome track.

Don't forget to book your train trips in advance (Tickets become available at around 6 months in advance and can save you a bunch of $$!)

If you want to save big $, fly roundtrip nonstop from JFK to Milan (MXP). typical prices in your window are $800 pp versus about $1400 for Rome or Venice. The train transfers on high speed trains are cheap and easy.

Check out the JFK - Milan flights with Emirates.

United's flight into Venice out of Newark is Summer seasonal, and it's very expensive. Delta also makes the flight out of JFK seasonally, but I don't know what the dates are.

But you can fly out of JFK Fridays on Norwegian Air Shuttle's new Boeing 787's into Pisa--Tuscany's largest airport. You could take a short train ride Pisa to La Spezia and on to Cinque Terre as a substitute for the out of the way Amalfi Coast. You could return home on Norwegian Air Shuttle from Rome to JFK every day but Friday--for a total round trip price around $700. That's maybe 1/2 the airfare of the legacy carriers. See Norwegian.com

Two weeks is not very long for all the places on your list, so you will need to be super organized.
I also think you will want to go the wedding with an Amalfi Coast suntan.
For your 4 days in Tuscany, maybe pick up a hire car in Orvieto and return in in Florence.

20 Sep - Arrive Rome - 3nts
23 Sep - Train via Naples to Amalfi Coast - 3nts
26 Sep - Train to Orvieto, pick up hire car. Drive to Montepulciano - 4nts
30 Sep - Return hire car in Florence - 2nts
02 Oct - Train to Venice - 2nts
04 Oct - Depart Venice

I agree with David that CT is a better option than the Amalfi Coast given your time constraints. Or, you could spend more time in Tuscany and/or spend a little time in Umbria. It really depends a little on your interests. If you can let people know what these are it may help.

Two weeks is not very long for all the places in your list
I totally agree with the advice to limit your destinations. Venice, Florence and Rome are already bordering on the too much. That's certainly the case if you want to do more than just have a glimpse of the usual highlights and to allow yourself some relaxation with a mid-afternoon gelato or an early-evening beer or wine on a terrace.
When in Montepulciano with a car, I can highly recommend you to put Orvieto, Spoleto and Assisi on your list for day trips. They can't fail to impress you.
When in Florence, Pisa is an easy daytrip on one of the frequent »regionale« trains, with Lucca as a free extra.
For train planning, the website of the Italian railways http://www.trenitalia.com/tcom-en is an easy tool when you remember to use the Italian originals for place names. It's also the place for advance reservation (some two, three months beforehand) of considerably discounted tickets for the fast »Frecce« trains on the longer distances.

Thank you for all your responses. I also agree that 2 weeks is not a long time, and given the wedding time spent in Tuscany will take up 5 days by itself, we definitely have to narrow things down a bit. Is there any thing we can do in day trips out of Tuscany? It is such a hard decision where to visit, because my heart wants to see it all! All your responses do help to put things in prospective. We need a car in Tuscany. If we fly into Milan and take the train to Florence, where is a good place to rent a car for Tuscany?
I appreciate the flight help also. Milan seems to be the way to go if I want a direct flight that is less than 1400 per person. I really don't want to waste time with layovers, though the option is tempting given the prices.
As far as sites we want to see... we wanted to see Rome, and the vatican is a definite for us. I don't want to spend too much time there tho. Anything else is just the icing on the cake.
We are in our late 50's and early 60's and in good shape. We love walking and exploring.

Orvieto, Spoleto and Assisi, good for a daytrip from Montepulciano, are in Umbria.

If wedding and Rome/Vatican are the priorities, I would do this:
Fly to Milan (for above reasons)- 1 night
Train to Tuscany/Montepulciano for wedding. Not sure where to rent a car, but no doubt getting there by train is easy. (5 nights)
Day trip to Florence while in Montepulciano.
Train to Venice, and I think 2 nights is plenty.
Train to Rome-4-6 nights
Add Amalfi Coast if time permits.
Leave from Rome, but if the Milan RT is way cheaper, just take the train up there to fly from Milan.

Chiusi might work well for your car rental.

Whilst I am of the firm belief that you should finalize your ground trip itinerary before booking flights to suit, sometimes price can be an influence and dictate some minor adjustments after careful consideration.
If considering American Airlines then make sure you check their One World partners (British, Iberia and Finnair) as pricing can be different for the very same flight depending on which website you go to.
Cinque Terre is a good alternative to the Amalfi Coast.
Arriving Milan, and departing Rome would appear the best choice.

19 Sep - Arrive Milan, train to Venice - 3nts
22 Sep - Train to Florence - 2 nts
24 Sep - Train to Cinque Terre - 2nts
26 Sep - Pick up hire car in La Spezia, drive to Montepulciano - 4nts
30 Sep - Return hire car in Orvieto, train to Rome - 3nts
03 Oct - Depart Rome

Just making sure if I take the train from Venice can I stop in Chiusi to rent the car?

A little more info for the hopper: American Air appears to have a direct flight from Philadelphia to Venice (was formerly a US Air flight) although it may be pretty expensive, like $1350+ r-t. Venice is a nice place to get over jet lag at the beginning of a trip, and would allow you to start north, finish south, without taking time and money to double back.