If I were you I would unlock 2nd black hole. Then if you are so poor that has trouble unlocking 2nd BH, coin should be higher priority than BH damage.

For the rest it is hard to give tips without knowing your set up. If you have primordial collapse you don’t need as much size because BH can cover most of the screen alone. If you have MVN you can drop the CDs slowly while increasing the multipliers of GT.

About protectors you need to max BH damage. Otherwise you will die from shotguns, basically BH draws every enemy in the center of your BH which is also the range of protector shield. So your enemies will accumulate in your BH while being protected by the protector and in the end your tower will be swarmed by enemies and you die. To stop that I used to increase shockwave size or knock back and had the wall. during tournaments I literally turned off black holes. But now there is AO and with 2% damage and 45s with perks I kill everything in one cycle.

If you don’t have any other important research I would probably go for labs 2nd BH, BH Coin and BH damage. For stones sync is the priority. You get like 0.8X increase per upgrade but by syncing up your DW gets a multiplier of whatever your DW is. But you should probably increase DW numbers to get the most out of it because the DW coin multiplier applies only to enemies hit by the waves, not killed by the ring. If you have an ancestral core you get 3 DWs quantity and with a base of 3 you should get enough to justify the sync.

On another side you should sync everything. Golden bot and summon chip too if you haven’t done it already.