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First should always be lab, get those upgrades started as soon as possible. DE drill is number 2 IMO. Then I say Clan Castle. Depending on how many builders you have use 4 and 5 to be making and upgrading all the new buildings that are cheap and don't take long.
After that initial spurt, I like to follow the order of splash, point, traps, walls for gold and basically whatever I feel like for elixir.
When reaching a new TH level, always prioritize offense. (Lab, spell factory, and army camps). In the case of TH8, it would only be the lab.
Next, get all your new buildings and walls up to the same level as your existing ones.
Then the clan castle. This upgrade is more important than most people give it credit for. It adds to your offense and your defense.
When upgrading defenses, do splash first. At TH8, I'd say do mortars before wizard towers. Level 6 mortars can 1-shot level 6 archers, which is important because at TH8, you will get smashed by TH9's regularly. Then wizard towers. They're expensive, but they really start to shine once they're at level 6. If your clan wars, do air defenses after that. Otherwise point defenses.
Getting your DE drills to level 3 should be a priority as well. 2 level 3 drills produce 2,160 DE per day.
Currently maxing out my base so just so you know teslas are your best friend. Do no neglect them because at max level they are awesome
Wiz 5, Pekkas, and Golems are unlocked in TH8
Hogs 4 and Dragons 3 too
if you're war active, and look to offense more than defense, you can clear the Barracks and Dark Barracks upgrade early
but Laboratory is definitely a must on any TH lvl
I build all the new stuff that is quick. 1 troop upgrade, start with lab, then a barrack or a dark barrack, 1 aoe damage (start with mortars then wizard towers), 1 point defense (I did archer towers then cannons), 1 air defense or tesla.