I am arriving in Europe in 4 weeks. I have never been to Europe so I am a bit over whelmed. I will fly into Zurich, travel in Switzerland for 7 days then on to Austria. Should I purchase a Swiss Rail Pass and then a separate train trip to Vienna? Or, a Eurail pass for 2 countries? Thank you for your help.
I would get the Swiss Rail Pass and buy the separate ticket to Vienna.
You haven't told us your detailed plans, I don't know where you are going or exactly what trips you will be taking, so no informed answer can be given.
But, for most people's itineraries (and I am not taking responsibility for this answer), the best plan is a Swiss Pass for Switzerland, and then individual tickets from the border to Vienna. The Swiss Pass has a slightly better coverage than a Eurail Pass, and Austrian long-distance tickets have discounts if bought in advance.
But, you do need to make a plan of where you will be each night. Have you booked hotels yet? 4 weeks is very late for planning, some hotels may be full and the cheapest Austrian rail tickets may be sold out on some trains. So act now.
For info on trains and where and when to buy tickets, see these two web pages
Do you have a trip plan for Switzerland? What's your priority in choosing a pass? If you plan to see a lot in Switzerland, then you'll probably get the most coverage, value, and convenience from a Swiss Travel Pass for 8 consecutive days. The pass covers you to border crossing points such as Buchs. You can book the one-way ticket to Vienna either while there or in advance for a discount.
I agree with the above three replies - a Swiss Pass is probably best. That's because a Swiss Pass has better coverage of many of the things that visitors come to Switzerland for (specifically, mountain lifts and travel in the Berner Oberland past Interlaken) compared with the two country pass. However, as everyone else says, you have to list what trips you are definitely taking and possibly taking, then look up the costs, then compare this with the various pass options. Yes it is a lot of work, but it's the only way to know for sure.