The character is describing himself with, I guess, a "sales pitch" on what is attractive about himself. What I'm stumbling on is:
How to take 甘さも渋さも in the context of physical appearance? Is he saying he doesn't look too soft but also doesn't look too grim?
How to take 看板店員 here? My take would be a male version of 看板娘 and not a literal someone who holds a sign?