Question: There are two worlds of more or less equivalent technological level, say a difference of only a few decades and no more than 50 years. A first contact event occurs and after the hoopla dies down trading starts. 

Initially, barter is the primary form of trade but this quickly becomes cumbersome.

How would the two economies first establish a currency exchange and exchange rate?

Some commodities are similar and occur in similar quantities, particularly minerals gold, iron etc. Other commodities are unique to one civilization or the other; plants and animals unique to each planet, unique tech developed by one and not the other.

Some restrictions:

* Both planets have one currency or at least a dominant currency (like the USD)
* Neither planet is in a "dominant" economic or technological position.
* Travel between the planets takes a few days
* There is a moderate level of trust in business dealings but it is not clear how laws apply to off worlders on each planet.

Ideas I've toyed with:

* comparable commodity-based exchange, ie. gold standard type exchanges, but this seems archaic for technologically advanced worlds and would anyone really want to transport heavy gold out of the gravity well of a planet
* some type of crypto type exchange, but this seems problematic with distance and not very conducive to trade as the price fluctuates

Answer: 
As bitcoin history shows, currency exchanges will emerge very quickly as soon as the currency is considered to have some nonzero value, despite exchange rate fluctuations. The rates on all these exchanges tend to quickly converge, and are used as a basis even for other people who trade directly. Even after failures of large exchanges like MtGox, the trade went on.

Unlike Bitcoin, you have equivalent goods on both planets (gold, drinking water, rocket fuel, ...), so trader can use them to calculate the estimated value of foreign currency. 

When the interplanetary trade gets non-negligible and it gets regulated, these exchanges gradually enter the regulated regime and precautions to stabilize the exchange rate are made. I assume here both governemnts view the interplanetary trade as something good or neutral, not try to stop it.
I was thinking, if they are different life beings and have different life standards and materials use, what they have in common? Because one of the civilizations could valerate gold, whereas the others simply don't care.
But what they have in common? 
Both have difficulties and cost to travel between their two planets. 
The exchange rate could be a trip from one planet to the other. **They can calculate the equivalent in 1kg per trip.** 

I assume that the cost of travel is more or less the same in each civilization while being a little cheaper for the most advanced one. But they are more advanced, is logical they have a more valuable exchange. 

For example:

A car cost 50,000€, and the European Union can put 1 kg in orbit for 9047€ (according to Wikipedia, Ariane 6 cargo capacity and approx launch cost are 10500 kg and € 95 million). The car cost (50000/9047 = 5.52) 5.52kg per trip.

Meanwhile, in Russia, they are selling a laptop, about 40000 Russian Rubles. The Soyuz have a charge capacity of 7200kg and a cost of 3200 million Rubles. 1 kg per trip cost 444444 Rubles. The laptop cost 0.09 kg per trip.

Those calculations are approximate and the capacity and the cost of the launches and capacity of the rockets are also approximate, the source is Wikipedia.

If we convert the currency (the laptop cost approximately 600€, 40000 Rubles), the car is 83 times more valuable than the laptop. So, 0.09 kg per trip 83 times more, are 7,5 kg per trip. The Europeans have they car for 5,2 kg per trip. 
**The exchange rate is 1.44 Russian kg per trip for 1 European kg per trip.** I think it's a good ratio.