Update route: Focus on gold generation.
Since gems could easily trade into gold generation(1000 gem -> 250 tech scrolls == 83 gold drop + 1 tech scroll. earn 1 gold drop per 12 gems in average), focus on gems generation is the first important thing.
After gem yielding are maxed (Cargo gem in PvP; daily mission's gem in tech, Cargo ship hp (buying this allows you kill more ships, which earns more gems than it costs. You could buy it in case you have difficult spending gems or killing cargo ships)), you should focus on gold generation.
For gold generation, alchemy is the cheapest one (1 gold drop per 6 gems), but needs an acceptable exp earning rate.
Buying tech ship hp and kill more tech ship could be a cheaper choice (roughly 1 gold drop per 8.77 gems) than buying chests directly. Thus in case your gems are not enough, you could firstly buy tech ship hp.
For beginner who want to reach wave 7500 ASAP (~2 months):
a) Do NOT spend real money, gems are very cheap (~2000 per week). If you could wait for a whole month, you'll earn lots of gems.
b) Do NOT spawn tech ship or buy chests before you could earn 5 scrolls from them (unless you want to waste gems), and in case you could spawn tech ships, you basically needs to go through the rightmost line and going as deep as possible, until daily gems are maxed.
c) In case you want to buy chests with gems, do NOT buying chests that cost <1000 gems (unless you want to waste gems).
I want to know if there is an "auto surrender" available when a higher level has been searched. without "auto surrender", presitage time will be 2x longer than the theoritical minimum time.
I wonder if "search" could add the recent "Enemy" at the top of the waiting list. I want to make the highest level on the top, but I could only find "sort asc" and "sort desc" -- they musy work manually..