Do not buy new heroes with medals if you can help it. They do not come with any enhancement, which means you just dumped a lot of medals into only gaining a new unit. In most cases the new unit isn't worth the strength you just sacrificed to gain it. My suggestion is only buy when that amount is very insignificant to your current income.
If you are overly serious about this game, consider having two different party setups; One for clearing up towards your highest stage, and another for progressing the more difficult stages.
Have at least 1 member of your party with AoE skills, it helps tremendously. However, do not over-do it, you still need focused attacks to kill tough bosses.
Do not worry about spending too much medals on members of your party early on. They will all still be used for arena, you need 18 heroes for that.
Once you have a rather strong and well rounded hero (the Demon for example), you should consider dumping all of your medals into it, and have the rest of your heroes 300-400 lower than the rest. That number is an example, but basically give every enchant possible to your main, and use the left over on the others.
Flying units can only be hit by ranged units. They are good counters to thieves.
Stat gains from evo abilities only apply to that character. Also only ones in your current party are applied.
While doing your dungeons, you might want to consider doing a difficulty you can fully clear instead of half way through your current one if you are behind on gaining the crystal bonuses. You can easily get 250 crystals a day from dungeons, the next tier up is much harder.
If you are looking for an easier way to decide between your 3 Evo stone options from dungeons, switch to the Hero tab and click the "Honor Coin store" button to quickly and easily see how progressed all of them are.
Initially, you want to spend them how I describe on the Store page. After you have a good amount of that, as well as all 10 artifact slots, I suggest you start to save up your crystals for the chest events. Spend on the 2500 10+1 chests. The units you gain from there can be remarkable, as well as star upgrades to others.
This upgrade allows you to stack 2+ of the little boss chest icon in the top left after killing a boss. This means that you can go AFK or get distracted for multiple bosses in a row and not lose their rewards. This also will open all of the chests at once when you click on it, saving you time.
A lot of the heroes you get early on are actually quite good! Some might not seem it, but because of their economy based evo skills, your income gains noticeable bonuses since you do not yet gain any/much from your artifacts. As stated elsewhere, AoE is fairly powerful in this game. Because of that, I find that having Elf Mage Napolde in my group was great early on. Gnome Thief Neslin is really powerful in his own way, between his fast attacks and very high dodge. The Undead Archer that you get for free starts out at a high star, and is also a nice unit! He has extremely high single target damage, as well as a magic damage party buff that allows your AoE heroes to do more.If you are deciding between healers, the Gnome Healer is amazing due to his shield skill. This often allows your units to take 2 hits before dying. My current 6 are Gnome Healer, Ice Dragon, Demon, Undead Archer, Death Knight, and Human Warrior.
When do I start to see higher qualities of artifacts?Edit
The quality of artifacts you see is based on your highest stage. You seem to first start seeing the higher quality as diamond purchases, and then later as normal materials you get from dungeons. I started to see 5* artifacts around stage 4500.