Below is a table of upgrades in tiers of importance for Town Hall 3.

Tier 1Rebuild Clan Castle.
New Army Camp (5 min).
New Gold Mine, Elixir Collector (10 sec each).
New Storages (10 sec each).
Drop Walls and Bombs (instant).
Tier 2Elixir Storages enough to hold 25.000 total.
Build Laboratory.
Tier 3Army Camps to level 3.
Tier 4Gold Mines and Elixir Collectors to level 6.
Storages to level 6.
Tier 5Build Mortar.
Max Barracks and all your defenses.
Town Hall to level 4!

Please note that Town Hall 3 is maxed out fairly fast and the only real priority over another is the Clan Castle and Laboratory over the rest.