To be sure, I'd try all three options, but remember you are writing to each index with every insert / update. (so indexing both fields will have to be more beneficial by a margin to compensate for the negative effects on write performance) Remember, it doesn't have to be perfect, it just has to be good enough to handle the system throughput without creating unacceptable UI performance latencies.
What I'd try first is A single index on the field that has the most distinct values... i.e. if Field1 has 1000 different values in it, and field 2 only has 20, then put the index on field1.