Rail Pass or Point to Point?

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I am using this site for the first time and grateful to have found it.  I hope you will be patient with me as I try to explain our circumstance.....We are in our 60's and trying to travel as independently as possible (no tours.)  I was in Europe 10 years ago, and my husband has never been -- so we are unshophisticated travelers.   Over the course of 38 days, our itinerary is, briefly, Istanbul - Bucharest - Budapest - Vienna - Prague - Paris  - Brussels - Frankfurt - Venice - Rome - Florence - Pisa - Nice - Lucerne - Zurich.   We plan to take night train from Istanbul to Bucharest and from Bucharest to Budapest.  I understand we cannot purchase tickets from Bucharest to Budapest until we are in Bucharest.  From Budapest, I read that a bus may be a simpler and less expensive way to get to Vienna.  And I found a very low cost plane fare from Prague to Paris.   I cannot seem to get to a place of comfort in making decisions about the trains, whether to purchase a Euraiil pass.  I have looked at the Global Pass, which would cost $885 each, I believe, and I do understand there would be additional surcharges.  But I have not been able to navigate the websites sufficiently of the individual countries to make a good comparison.  I would appreciate any help you may offer.

We would probably not recommend to use Eurail pass for all your connections, because in most cases there are much cheaper way to travel. Let's take a look at budget options:
Istanbul-Buchurest: regular fare on this route is only 38.8 euro (50 USD)
Buchurest-Budapest: discounted ticket start from 29 euro (seats) or 39 euro (couchette), but you need to buy those in advance. Regular tariff - 50 euro (65 USD). For Istanbul-Buchurest-Budapest route you might as well consider Balkan flexi passa (>60 years old - 69 euro for 5 days of travel). But it can be used only till Romania-Hungary border, from there till Budapest you'll need another ticket (around 15-20 euro).
Budapest-Vienna: bus is a good options in case you want to buy tickets in advance, but train is more comfortable and can be as cheap as bus - discounted one way tickets start from 13 euro, but once again - you need to buy those at least 3 days in advance. Regular tickets start from 25 euro (32 USD)
Vienna-Prague: just buy discounted ticket online in advance - ticket.oebb.at (from 29 euro or 38 USD)
Prague-Paris: you are probably right here, cheapest option will be low-cost airline ticket bought in advance.

Rest of your itinerary are kind of tricky, since those countries you want to travel in (France, Belgium, Germany, Switzerland and partially Italy) tend to be quite expensive in terms of rail travel, thus Eurail pass might be an option if you aren't sure about exact travel dates and don't want to buy ticket long before the journey.
But if you can be strict on dates of travel and know them in advance, then you might "hunt" for discounted tickets. For instance,
Paris-Brussels: can be done for as low as 25 euro/32 USD (www.tgv-europe.com/en/)
Brussels-Frankfurt: can be done for as low as 39 euro euro/50 USD (http://www.b-europe.com/Travel)
Frankfurt-Venice: from 43 euro/56 USD (http://reiseauskunft.bahn.de/bin/query.exe/en?newrequest=yes&protocol=http:&)
Travel fares for trains in Italy really depend on type of train you choose and how long in advance you purchase, so you can travel Venice to Rome for as low as 19 euro or as high as 73 euro (http://www.trenitalia.com), Roma-Florence (from 16 euro and up to 44 euro). Florence-Pisa is easiest and cheapest part - standard fare of 5.8 euro only. Pisa-Nice can be done for as low as 20 euro.
Nice-Lucerne: French railways don't offer any nice fare here, so this part might be the most expensive one (let's say around 50 euro with change in Geneva)
Lucerne-Zurich: from 7 to 23 CHF

Resume: as you can count yourself, smartly bought in advance point to point tickets will cost app. half of the Eurail pass fare (we counted around 450 USD in total), but those tickets in most case will be non-refundable + you will not be able to change date of your travel and you will need to buy almost all the tickets in advance. 

Another solution for you is to change sequence of destinations in such way that you can save even more on point to point tickets. For instance: Istanbul - Bucharest - Budapest - Vienna - Venice - rest of Italy - Nice - Paris - Brussels - Frankfurt - Prague - Lucerne - Zurich or Istanbul - Bucharest - Budapest - Vienna - Prague - Frankfurt - Brussels - Paris - Nice - Italy - Switzerland.

Thanks for your prompt response.  We have examined and re-examined our itinerary, but because of some visits planned, it is difficult to change.  Thank you for the links.  We are going to try to stick with point to point reservations, although that means some arrangements may not be possible until we are actually in Europe, which makes me a little uneasy.  We have been unable to get any fare quotes from Vienna to Prague from the website you mentioned, but some of the other ones have been very helpful.  Thank you again for your help. 

...although that means some arrangements may not be possible until we are actually in Europe, which makes me a little uneasy

The only tickets not available online is from Istanbul to Buchurest, Bucharest-Budapest and Budapest-Vienna. Those routes aren't that busy, especially if you book couple days in advance, so we wouldn't worry that much. Just go to the ticket counters first thing after arrival to Istanbul, Buchurest and Budapest respectively. All the rest of your connections are quite easy to book. Connections like Florence-Pisa is not worth even booking in advance, distance is too short, too many trains + anyway you'll pay full fare. Similar thing can be said about Pisa-Nice if you choose budget option - use of regional trains till Ventimiglia + international ticket for short Ventimiglia-Nice part. 

We have been unable to get any fare quotes from Vienna to Prague from the website you mentioned

It is probably technical thing, try here - https://ticket.oebb.at/bin/frame_ticket.pl?ticket=jticket.pl&LANG=EN (checked, this one works ok)

Anyway, if you have any further questions feel free to ask here 

p.s. small addition for Brussels-Frankfurt connection: rechecked and found out that on German rail website (reiseauskunft.bahn.de) those tickets available even from 29 euro, instead of Belgium 39 euro fare.