Alright so this should be the order in my opinion
All these buffs are the main buffs, they affect arena gameplay
1. HP. Get this to level 10 asap and thats free 300 HP. Really really really helpful. The 11th upgrade costs 2k arena coins so do that upgrade late game
2. Elemental Damage (depends on the type of mechs you have)
3. Energy Damage/Heat Damage is you're a heat/energy main
4. Heat Cooling/Energy Regen/Heat Capacity/Energy Capacity
5. Resistance (all 3)
6. If you have backfire items, backfire reduction
7. Now you can save for 2k coins for 11th HP upgrade
Now, there are other buffs which don't impact arena gameplay
1. Fortune Boxes
2. Fuel Regen/Fuel Capacity
3. Crafting cost discount/Craftng duration speed
4. Arena Gold/Campaign Gold
5. Upgrades duration speed
6. Titan damage
7. Titan rewards