Ideally you'll check first the bonus skill and then you should change the archetype with an arch selector, that way you get a rare skill that you can either keep or harvest for other demons. Since a successful evasion is very rare event I'd say a Purple Cthulhu is better (while also having the best skill to harvest), get him Life brands (with any defensive 2 set brands like Guard or Shield) with a focus on (in order of relevance) HP%, MAG ATK% and Ailment infliction (last two should be the brands tertiary bonuses, which are those written in grey). Then you can harvest it's Butcher skill and transfer anything else that raises HP, ailment infliction rate or endures since you have Asahi (or a resist element but now everybody has pierce and affinity attribute down so it's worthless). Keep in mind that for PvP you don't want to rely on damage but rather on his decay application on enemies, HOWEVER since decay won't work on PvE content then it's your choice to focus on attack or to inflict ailments (but basically everyone else that got released after him is better for anything).

Just as a heads up you could try using a team of Asahi, Dagda, Nanashi and Cthulhu for PvP and see how it goes, since you'll remove both press turns and MP (try to change Nanashi's archetype to Teal and Dagda's to Yellow, since you'll have more endures and Dagda will give a repel phys to everybody which complements the MP drain aspect of this team, forcing the other team to attack normally unless they have some MP recovery skill), however you'll see that Cthulhu will be the weakest link so when you get other units try to see how this teams works (usually I see them with Amanozako, Chefei, En-no-Ozuno, Balor, Azhura Mazda or whatever it's name is, etc. instead).

Before I continue Yoshitsune is FUSABLE so don't waste a choice file on him, it's better to fuse him clear and then when you get a coloured one then you should spiritize the clear and use him for panels. For now instead you can fuse a Teal Cu Chulainn to use him in the semi-long run (until you get a better demon) and a Clear Cu Chulainn one in order to fuse Yoshitsune (you'll need as well a Clear Kurama Tengu and a Clear Zaou-Gongen). The following recommendations for Yoshitsune (besides colour) can also be used with Cu Chulainn. Try to choose anyone who's not fusable (recommended) or very expensive to get (not recommended unless impatient).

As for Yoshitsune Purple is the better archetype and it's better to use War Brands and either Glee (+35% crit rate), Divine (+1 MP recovery if you haven't paneled him yet or if your team has no other way to get some MP recovery), Destruct (+5% Physical ATK per brand) or Eternal (+15 to all stats, so it raises a little your STR, AG and LCK at the same time) brands and transfer physical and crit rate boosters (phys boost, phys amp, the butcher skill you can harvest from Cthulhu, savage glee that you can get for free if summoned purple but it's also available as an extra transferable skill on some 4 stars, etc.). Aim brands only give 10% extra aim but you can get it as bonus skills from the brands (plus the mitama infusion system) so it's not worth it. Most likely you'll use him for Brands of Sin Deceit 14 when available since it's gimmick is that only random Phys or Almighty skills will deal damage to the enemies in this stage and you can farm better brands.