Below is a table of upgrades in tiers of importance for Town Hall 2.

Tier 1Add every available building.
Elixir Collectors and Gold Mines to level 2.
Tier 2Elixir Collectors and Gold Mines to level 3.
Storages to level 2.
Tier 3Army Camp to level 2.
Elixir Collectors and Gold Mines to level 3.
Storages to level 3.
Tier 4Town Hall to level 3!
Upgrade defenses if you got idle workers.

Please note that Town Hall 2 is maxed out very fast and it’s more about trying to sync the upgrades with when you are able to play than tiers of importance.