Of the four that you mention, the Integrity is the best. However, you are all over the place with these choices. I would consider the 200 series only if you don't have any high exposure.
Do you have a budget? That is where I would start. If you do not have the budget for Integrity, there are much better vinyl choices than Jeld Wen.
After deciding on a budget, I would visit showrooms and see what you are going to get. You will be living with your choice long after the contractor is gone. It will not be a simple choice so prepare yourself.
You should get plenty of feedback here so take your time.

+1

My list would be Integrity (or Infinity in the replacement series) and the Andersen 200.

If you are considering vinyl, ditch the JeldWen and look for Soft-Lite, Okna, HiMark, or Sunrise.

I did visit Home Depot and looked at the Anderson 200/400 and JeldWen. The sales guy there told me that the Anderson 400 is a much better window than the 200. For a home that you plan on staying in, he said the 400 is a better choice. Same advice from my contractor. I've also looked at Harvy windows, and did look at Marvin, but that was a few years ago. I like the idea that Anderson is a wood window, but no maintenance.

I don't put much stock in any recommendations made by HD employees. That said, the 400 is not a bad choice. I would concur however the the Integrity is probably the best choice of that bunch.
What are your goals for the project? Performance, warranty, appearance, cost, maintenance? Your answers to those questions will determine which material (vinyl, wood, fg) is the best choice for you. If you are not averse to the appearance of premium vinyl, it can be a very difficult choice to beat, and WoW just listed the creme de la creme of vinyl choices... If you just don't like vinyl, the Integrity does offer a pretty appealing package overall.

I have the 200s in my home (it was built with them) and they are not a drop off at all from the 400. I have seen neighbors that upgraded to the 400 for the tilt functionality and they have had more complaints to be perfectly honest.

I would figure out what you want the windows to look and feel like and work backwards from there.

Here an update:

My contractor said that I could use Anderson 200s for the 8 double hung windows, but that he wasn't sure he could match the size exactly. The 400s are available in more sizes. He also said that the bow and awning windows I need were only available in the 400 series. He took off the molding on one of my double hung windows and said that they did a really good job installing the window (i.e. no gaps, etc), and it got me to thinking that maybe I should just have replacements put in, instead. My 1959 house was very well constructed. Ripping out all my old windows and putting in new requires a lot of finish work on the inside.

Appreciate any thoughts on this?

In addition, I was told at the Marvin/Anderson showroom (a local hardware/lumber yard) that vinyl isn't the best choice for this part of the country because of the temperature changes, wind, etc. Appreciate your opinions on that as well.

bump

Not true at all, a quality vinyl product will be fine in just about any climate shy of the arctic(and maybe even no issues there).

What is your part of the country?

Inserts will probably be just fine in your application and will be more cost effective.

Vinyl does just fine in about nearly every application in this country and most of the most air tight windows on the market are in the vinyl family so that is not a valid rationale.

I am going to guess she is in Connecticut wow.

Ah...yes!

Missed the inCT part.

Nothing about vinyl that isn't perfect for that climate.

Just put a bunch of Okna EnviroStar windows in my Sister in law's home in Glastonbury this week. She is loving them.

Yes I am in CT... good guess. Understood that a vinyl insert would work, but if I'm replacing the siding, is it best to go with a new construction window, understanding that its going to cost a bit more due to finish work on the inside, or save a few bucks and go with the insert. My contractor said that the windows I have were installed very well.

If you are doing siding, new construction is a great option and will allow you to get a bigger opening and more secure water management details.

Looks like everyone agrees that new construction is the way to go, so I'm probably going to go with the Anderson 400 new construction windows. I may have him price out the Marvin windoes as well since everyone seems to think those are so much better. Also, 've decided to wait until spring to do this... I don't want to be replacing windows in January.

Any more thoughts on wood vs vinyl in CT?

Well built wood is fine for CT and any application for that matter as is vinyl.

You will find more high performance windows in vinyl that you will in wood and they are certainly okay for CT temps.

higher end vinyl such as Okna, Soft Lite, Sunrise, and HiMark would be your best bet for structural integrity as well as performance/ energy efficiency.
the Okna 800 is a beautiful window and actually looks like a wood window when installed. ive installed this window in many older homes in very exclusive neighborhoods. higher end vinyl will not detract from your home like lower end vinyl offerings from home depot, lowes, and the junk most local contractors offer.
in wood, andersen 400 is a pretty good window as is the marvin which i really like. harvey wood windows are junk and ugly in my opinion.
for new construction, just bear in mind that you will need to rip out all of your interior moulding. this can be problematic in older homes with unique moulding detail.

+1. As I mentioned earlier, wood and vinyl can both be very good choice, and your goals for the project will determine which choice is better for you. If appearance is paramount, then wood will have an edge. Premium vinyl typically wins however in the "value" proposition, as it will provide superior performance/efficiency, warranty, less maintenance, etc... 99 out of 100 people that are open to considering vinyl end up going that direction.
One last thing to add, is that in insert vs full tearout (new construction), mmarsel brings up a good point that was not mentioned earlier, and that is the disturbance of your interior woodwork. That should be weighed as well.

I've got clamshell moulding, so nothing that special. The contractor is suggesting putting in wider moulding in its place. Remodeling decisions can be overwhelming, but at least I've got time to think about it. It can drive you crazy.

Maybe I should just fix my existing windows installed in 1959 (replace any cracked glass and rotting wood), along with the storms? I've heard it will take many many years to recoup the $$ spent on windows in savings you get on heating costs.

the money, time, and energy wont be worth it. also, although true that it may take a while to recoup dollars, you have to remember the comfort issue. your home will be much more comfortable with new windows and you will definitely be enhancing the look of your home as well as adding value.
doing it the other way really makes no sense in my opinion.

As mmasrel has said, don't underestimate the cost of renovating your existing windows along with storms and possibly capping. I usually recommend that route only for historic homes that are attempting to preserve the distinct character of the home.
The contention that windows do not pay for themselves in energy savings--and therefore the are a bad investment-- is typically an overzealous response to the sleazy salesguys that try to sell on that premise. New windows offer increased comfort, ease of use, improved appearance, increased property value, etc, all while improving energy efficiency. Nobody says that remodeling a kitchen is a bad investment because it does not pay for itself in energy savings, and using that logic on windows is just as ridiculous...
Your contractors suggestion of wider interior trim is a good one if you do go the full tear-out route.

Thanks everyone, I appreciate all your input.