Eurail Pass or Individual Tickets?

Most people find that a train pass rarely is cost-effective. For some of the trains, you will have to add seat reservation fees on top of the cost of the pass.

However, do the math. Go to the national websites and price out your tickets. For example, you can use bahn.com for any train that starts or ends in Germany and you can use trenitalia.com for your Italian trains. You won't be able to look up dates in the fall so for estimating purposes, just look up the price for a date in the next week. The websites will typically list standard priced tickets and discount tickets. If you can nail down any dates, you can potentially save money by buying a discount ticket. If you can't, then just factor in the cost of a full price ticket.

Without knowing your dates, any estimate will be merely a guess. The only way to accurately evaluate a pass is to start at the other end by calculating the point-to-point costs. Here are your basic tools:
www.seat61.com will provide links to national rail operators and provide advice on ticket strategies.
www.bahn.com is the German system which provides timetables for many countries although it can only sell services connected to Germany.
www.skyscanner.com and www.whichbudget.com find low-cost plane tickets.
In general, flexibility is expensive, especially in busy times of the year. Some of the major trains are much cheaper bought well in advance, including seat reservations if required. And I do mean much. Or some trains may be full, not common but certainly possible. Ditto for cheap flights. Freelancing it, as you hope to do, really is better by car than public transport.

I found these prices plugging in random dates, but if anything your actual cost will be lower - not higher
- Vienna --> Bratislava (hydrofoil): 23€. Be aware that it only runs W-Sun in September, and the river is sometimes too low for it to run. If you do have to take the train though, it'll be around 11€.
- Bratislava (the station is hlavna stanica) --> Budapest: around 15€
- Budapest --> Zagreb: around 50€
- Zagreb --> Split: around 63€
- Split --> Rome (airplane) [as low as 50€ on easyjet - check skyscanner.com. just make sure to follow their baggage rules strictly or you get hit with lots of extra fees]
- Rome --> Pompei: around 13 to 50€ depending on how fast/what type of train [note: I would think about staying in Rome or Naples and just making Pompei a day trip. I'm not sure if there are many places right around Pompei to stay.] All of the Italian prices are found and can be purchased on Trenitalia.com
- Pompei --> Amalfi Coast: around 2€ on the Circumvesuviana railway.
- Amalfi Coast --> Florence: around 59-86€, take the Circumvesuviana back to Naples, freccia to Florence.
- Florence --> Venice: around 27-45€.
- Venice --> Innsbruck: around 50-66€
- Innsbruck --> Munich: around 34-37€.
- Munich --> Salzburg: around 19-32€.
- Salzburg --> Vienna: around 55€

Taking the high estimates (although you could go much lower) it would be around 564€ or $774 (at the current rate). I don't know that a pass would cover every piece of the route, like the hydrofoil. But even at the highest estimate, a pass would not be worth it. If you can commit to certain routes and times ahead of time, buying non-exchangeable non-refundable tickets, you can save lots and lots on many of these routes like Naples to Florence, Florence to Venice, etc.