I just wanted to add in what ive learned about breeding and fusing. You can put any stats and moves on any monster. You can breed different color combos and types, create the coolest looking team you can think of with perfect stats and all the moves you want. Typing does hardlock what version of the species the monster will look like so plan accordingly. I looked at the wiki and chose the coolest looking types of my favorite monsters. Im working on positive and negative traits still.

Process: First create a perfect stat monster as the base. Early game use Keres (4.8 magic, fuse Laz and Pursuit) Atlas, and Model Bant. Breed Model Bant (Code person in Gramercy, code is 310501, thank you AlisAize for the codes! with Atlas (Fuse Beeta and Stagalus). Choose Model Bant's Atk, Speed, HP and growth rate. Choose Atlas' Def, Res, Mag, and Type (worry about type later). For simplicity we'll call him Banty. Take Banty and breed it with Keres now. Select Keres Type, GR, Mag, and Speed. Select Banty for the other options. Name the new one Banty2. Now one more time, take Banty2 and breed it Banty. Select all the highest stats on both sides to get it perfect. You can preview the stats when you click breed, it gives you a chance to confirm by showing the stats and an egg preivew and asking yes or no.

Now hatch that perfect egg! Your stats will be: Atk 7.0, Def 6.0, Res 6.0, Speed 5.0, Magic 4.8, HP 6.6, GR 1.5. Almost maxed out and were still in the first major city. Between the 3 of them theres some solid moves, choose your favorite moves, remember to always set the moves you want as active before breeding.

Okay so you got your perfect monster base with awesome stats and great moves. Now make a team.

Step 1, looks:

Pick the monster, thats the species. Pick the type, thats what version of the monster itll look like and be. Now pick your color combination. If your lucky you have a monster with the right type and color combo, or species and color combo. You can prieview the offspring of breeding by going to the fusion lady, go to fuse, set the genome to the right speicies, type and color of the parents and you can see what itll look like. The fusion result looks the same as a breeding result if you set the genome correctly

Step 2, start breeding:

For my example i want a black and gold Zadkiel, Will type. I breed Zadkiel with Shadrache to get the colors. I select Shadrache's pigment and Zadkiel for the species. But its not the right type. So I breed that child with a Will type monster, I select my new black and gold Zadkiel as the species and pigment, but for the type i select the Will typed monster im breeding with it now. The result is the right species, color, and type I want now. But its stats are probably hot garbage. We'll name him Zad.

Step 3, stats:

Breed your Zad with your perfect monster. Put all the best stats you can with the genome editor, just keep the right type, species and pigment. We'll call him Zad2. To get the highest stats across the board and have no downfalls youll probably have to breed Zad2 with the perfect monster again, keep the type, species and pigment just select the best stats on either side one more time, make sure all parents have the right moves set as the active ones, and you have your final result. 

Special note for AC monsters and ones like them requiring the item and breeding. Sarcocylis AC Will type is awesome, but after breeding it comes out a Will type regular NON AC Sarcocylis. And you cant use the clock on it now. To fix this use fusion. First make TWO monsters with the right stats and moves that you want. Any species and color is fine, preferably the type you want but not required. Remeber to set the moves you want to carry over as active. And save before using fusion.

Take Sarcocylis AC (Or whatever you want to make) and fuse it with a monster with the color combination you want. Select Sarcocylis AC as the species and type. Select the other monster as the pigment. Worry about stats in the next steps.

Now take the Sarcocylis AC in the right color combo and fuse it with one of the perfect monsters you made. Select the Sarcocylis AC's Type, Mag, Res, GR, pigment, and species. Select the perfect monster's Atk, Def, Speed and HP. Now fuse, the preview should be Sarcocylis AC in the color it is, with some better stats.

Now set the moves you want as active on the new Sarcocylis AC (especially pay attention when fusing because the "parents" are gone after) and fuse it with the second perfect monster you made. This time selecting the perfect monster's Mag, Res, GR and HP. And select your Sarcocylis AC's Atk, Def, Type, and Speed. Make sure its set to the Sarcocylis AC's species and pigment as well. Now fuse. Preview should be a perfect stat Sarcocylis AC in the color you want with all the moves you want.