"...is it just as easy/economical to rent the car in Amsterdam and go straight from there?"
You will pay a heavy drop-off fee if you rent in the Netherlands and drop in Germany.
Since you ask about costs, you should also inform yourself on vignette fees for Austria and Switzerland - you can't drive there without them, I understand.
Train fares to Germany: You didn't say what your plans were exactly - just Munich was mentioned. You can get from A'dam to Munich by train in 7.5 to 8.5 hours. There are still some €78 fares for that route (that's for two adults one way, so double that for 4 adults) for late September. Then you wouldn't have to rent a car (not that you HAVE to rent a car at all, but it seems you want to) until you're done with Munich. A car in Munich is useless.
If your plan is to explore Bavaria, make sure you rent a car with adequate luggage storage for 4, of course. Alternatively, the Bayern Ticket day pass provides nearly unlimited travel around all of Bavaria and in parts of Austria for €38/day for 4 adults.
Bayern Ticket info