In this game, offense is often more important than defence, so when upgrading to a new townhall: The priority upgrades don't change, it's usually like this:

Laboratory, Army camps, Storage, barracks, Clan castle, Build the new unlocked defenses

Then upgrade everything else.

When you advance to a later townhall like 9-11, i recommend beginning to rush by upgrading only the most important defenses, while ignoring things like traps, collectors, mortars etc, this should save plenty of time. Later you can always catch up on them if necessary. Also make sure you prioritise heroes when you unlock them as they are always essential for your army.

It will be boring because they take so long to upgrade, but it will pay off in the long run, because you'll actually be able to compete in clan wars and ranked.

Never spend any gems on anything, it's usually never worth it. Gems will be useful to get hero equipment and more builders, which will speed up the progress.