Immediately after TH7 finishes, you should obviously build all the new buildings. Among the most important is the new Army Camp; the extra space will undoubtedly be worth it. The 4th Barracks, while useful, is not quite a priority.
The 3rd Mortar and 3rd Air Defense as well as other new defenses can play a big role in keeping your base safe.
Get the Dark Elixir Storage and Drills, you'll need all the help you can get to unlock the Barbarian King. Without the DE storage you can't unlock the Barb King (your TH can hold only 2.5K at TH7).
Additionally get the Dark Barracks, you never know when you'll find Minions and Hog Riders useful at TH7 (Minions are good at farming and supporting Balloons, and Hogs could work surprisingly well).
As for new things to upgrade, definitely the new level for Lab and Spell Factory first. Practically all TH7 troops get upgrades at level 5 Lab and the Rage Spell will definitely be a boon. Even if you do not intend to use the Rage Spell, the fact that you can fit a 3rd Elixir spell will help loads.
If you're feeling the need for upgrading your defense, by all means go for the splash damage upgrades (Mortar and Wizard Tower) as well as the Air Defenses. The new defenses will also need catching up too, keep those in mind too.
Offensively for war, get the barracks to Dragons ASAP. Its the quickest way to take a real army to war. Otherwise, get your loons up and get minions for both farming and war.
I would say teslas would be the most important of the defenses, all around. They target both ground and air, deal huge DPS and are a surprise for the enemy. Teslas, along with archer towers and AD have a shot at defending against mass dragon.
Spring traps lvl 2 is a huge boon against valks (not that you would be too worried about that at TH7, just saying).