Gold Summon

You get 5 of these for free every day. It is possible to summon full heroes with Gold summons but extremely rare.

Get your free pulls, complete the daily quest, then forget about Gold summons. Not anywhere near worth the gold cost at any stage of the game. Opinion by AzakaZero

Incarnite Summon

Incarnate summons yield better results than gold summons, but are of course not as good as Special summons. It is possible to summon full heroes with Incarnate summons but extremely rare.

Always do 9+1 incarnite summons. It's a 10% discount, and you can't be that much in a hurry. Opinion by AzakaZero

Special (Crystal) Summon

You get one of these for free every 2 days.

Only ever summon with crystals if there's an ongoing event that guarantees a hero (or something else you really need) is included in the summon. Of course, if you are filthy rich and very impatient then you can do whatever you want, I won't argue. Opinion by AzakaZero