Chaos Campaigns are an extremely important part of Castle Age. If you want to become strong, Chaos Gems are mandatory.
So you may as well want to complete them in the most efficient way possible, which will vary depending on your build, playstyle and spending habits (among other things).
Strategy on getting Gems
The best long term strategy, especially if you don't want to invest too much or any resources on Campaigns, is probably to start Hard Campaigns every two weeks no matter what, and complete only the tasks that suit you to get Epic Shards.
Because not only do harder Campaigns give Shards of a better rarity, each task also gives more Shards. For instance, if you complete one Hard Campaign top-row task, you will get 60 Epic Shards; while if you complete one Easy Campaign top-row task, you only get 20 Common Shards! Knowing that you need 9 Common Gems to end up with a single Epic Gem, you can see the huge gap between those two rewards. It's much easier to get Epic Gems from Epic Shards than from Common and/or Rare Gems.
To give you another example, if you complete all 6 top-row tasks of a Hard Campaign every time, you will get an Epic Gem every 6 weeks. While if you fully complete Normal Campaigns every time, you will get a Rare Gem every 2 weeks, but that translates to an Epic Gem also every 6 weeks. The difference is that you will need to complete all Monster tasks of the Normal Campaign in order to achieve that; while you can completely ignore them in Hard Campaigns for the same result. And Monster tasks are usually by far the hardest tasks for most players.
However by fully completing Normal Campaigns you will get immediately useful Rare Gems instead of just Shards for partial Hard Campaigns, so if you don't mind the Monster tasks it may be better to do Normal Campaigns.
And of course, the best is obviously to fully complete Hard Campaigns for an Epic Gem every two weeks if you can and want to do so.
For the vast majority of players however, the Monster tasks will require many refills or Full Potions, and you will need to complete all 6 top-row tasks as well, a few of which may be very hard to complete. All in all, it will require much more commitment to this part of the game (compared to just collecting Shards by completing the top-row tasks which aren't too difficult for you).
On the other hand, if you're too low level for any of the Normal or Hard Campaign tasks, doing Easy Campaigns is still much better than nothing!
Strategy on completing individual Tasks
As for the top-row tasks themselves, many are easy or even really easy even in Hard Campaigns (e.g. "Acquire Wood", "Use Heal", "Use tokens in Land of Mist"...).
You should definitely buy all Class Powers required for Campaign tasks (Heal, Polymorph, Whirlwind, and maybe Evade although it's harder to complete the 200 actions). You only need the first level of each Power which costs 1250 Guild Coins, and it's extremely worth it even if you exclusively use some of these four skills for Campaign tasks. You can complete the related tasks in Guild Battles, Conquest (LoM and LoE), and Colosseum when it's available.
Some other tasks can be very easy or relatively hard depending on your Conquest Level (and thus the max amount of tokens you have and their regen rate) and your Guild Level, for instance "Collect Mithril Medals in Conquest" or "Earn Blue Crystals".
On the other hand, certain tasks may require some planning. For instance, you can stack your Hero Potions and use them when a Campaign task asks you to. Same goes for Essence trading. Those can be very easy with very little planning.
It can also be done for "Earn Hero Crystals": stack Hero Dust and use it and/or buy Hero Crystals from the Conquest Path Shop only when this task comes up; or you can even use the "limited time" alchemies (although be careful, they represent an extremely bad trade for most players).
The "Level up your Hero" task can be really hard but planning can help as well: keep the acquired heroes you don't use at level 1 and level them to 4 or more when this task comes up. However it may be harder to manage consistently.
A few tasks may be really hard or impossible to achieve without spending depending on your build, such as earning Red or Green Evolution Crystals. Some tasks you may not find worth completing, such as "Spend Stamina on Siege Weapons" or getting Demi-Points from a Demi-God you're not interested in praying to. Some may be very annoying to complete but not necessarily hard, like "Kill Enemies in Duel/Invade" (which can only be achieved in regular Battle).
For the "Earn Demi Points" tasks, there are ways other than praying to the corresponding Demi-God to earn them: check the Demi-Point article for more info.
Legendary Chaos Gems
It takes 4 Epic Gems to craft 1 Legendary Gem. As such, you should create a Legendary Gem ONLY if you have 4 Epic Gems which you have absolutely no use for.
The reason is that even though Legendary Gems are the best Gems, even just 2 Epic Gems are still better than 1 Legendary Gem (unless you have very bad secondary powers on the 2 Epic Gems and get awesome secondary powers on your Legendary Gem - but you don't know what you're going to get). It's infinitely better to have 4 Epic Gems equipped than just a single Legendary Gem.
Furthermore you can get Unbind Stones easily from the Colosseum Shop. Which means you can very well forge many Epic Gems on your Equipment and remove them using Unbind Stones later to use them as ingredients to make a Legendary one.
Lastly, don't forget that Legendary Gems can only be forged on Legendary Equipment.