Eurostar is the only way you can travel by train between London and Paris so you have to.

As for the rest, rail passes are popular - but they aren't the bargain they were 20 years ago as they require supplements on the likes of the TGV, Thalys and most of the premier train services. So generally point to point is the best option.

I refer you to seat61.com who knows more about train timetabling than any one person should know.

If you buy your Paris-Amsterdam ticket far enough in advance it will be cheaper than a Eurail pass would be.
Passes are only worth it if you are travelling a lot by train, or don't want to be tied to a particular train.

Have a look at the prices of point to point tickets and work out which is better for you.

If I remember correctly, the Paris to Amsterdam trains have a heavy supplemental charge for those attempting to use passes and pass benefits for the Eurostar are minimal. Sometimes Raileurope has competitive pricing on the Eurostar but otherwise avoid RE as they are sharply more expensive and do not typically display complete schedules.

Paris to Reims tickets cost little more than 25€ each way.

For pricing information:

www.tgv-europe.com
www.voyages-sncf.com (in French only)

Paris-Amsterdam tickets go on sale 3 months in advance and are cheaper the earlier you buy them http://www.thalys.com Good idea to notify your credit card before attempting to buy on line.

In 2007 it cost 100 euros for a ticket at the last minute. In advance prices are as low as 30.

the only railpass you would consider would be a France-Benelux Eurailpass, valid in France, Belgium, Netherlands and Luxembourg - but you are not nearly traveling enough with just those trains to make it pay off - not even close so just buy the Reims return tickets once in Paris and yes the Thalys Paris to Amsterdam ticket way in advance online to get the often hard to get and limited in number deep discounted tickets - just show up and you may well pay $100 or more more

Great sources of info on European trains - www.seat61.com; www.budgeteuropetravel.com and www.ricksteves.com - you may check U S sources for Thalys tickets as well as at times RailEurope offers limited in time specials on Thalys that can be as cheap as online discounts - for any RailEurope product I always advise calling Budget Europe (2nd site I list and talking to Byron - an expert I have bought railpasses from for years and then compare Thalys prices in dollars to those online - www.thalys.com or www.voyages-sncf.com for Thalys online ducats.

Like the other posters said the value here is in travelling lots (on regional trains not high speed trains) to make the price of the pass worth it.

The only real way is to compare the price of point to point tickets in advance and see if it's less than the railpass with the reservations. If you're travelling in September, you can book your Eurostar around 120 days in advance and other trains around 92 days at least.

and yes with the Eurostar Chunnel trains the early bird does indeed get the worm - literally pay hundred bucks or more more if you just show up and buy a ticket - sold in tiers - cheapest tickets very limited in number so to guarantee book as early as possible.

the absurd seat reservation fee/supplement charged to railpass holders - $35 or 40 on top of using a day on the pass rules out any railpass for what the OP has outlined as a relatively few trips. The OP should not even consider a railpass for plans outlined.

Thank you so much for your advice. SO helpful!! We have booked our London to Paris train and once available (3 months in advance) we will book our Paris to Amsterdam pass.

Now for the Paris to Reims day trip we want to take - did you mean to just book it once we are there or should we book this in advance? Just want to make sure I understand.

Thanks again all!

I have seen Eurostar tickets sold up to 5 months in advance on Rail Europe (which is the only thing one should ever consider purchasing from them). If you wait for a 3 month window, you´ll most likely pay more than you need to.

The SNCF (French Rail) has eased recently the 90 day pre purchase window and you may now need to purchase ticket up to 120 days in advance for best prices.

Depending upon the train departure, you might save from 5€ to 6€ on each Reims/Paris leg if you book in advance but you can answer all of these questions yourself by simply using the websites previously suggested, plug in your travel criteria, and take a look at the price and schedule results. It´s really not that difficult:

www.tgv-europe.com
www.voyages-sncf.com (in French only)