Angel sounds way too basic bitch. Demon is about the last thing I'd normally play, but I might consider it given that you both mention it as good.
Build-wise though, I have no idea what I'm going to for. Prolly gonna spent my entire weekend on the character creation screen, so any great ideas you have are appreciated.
You could have a lot of fun with a Feral Champion Demon. They get claw attacks which scale with level, and you can have bite, gore, and other natural weapon attacks scale up as well if you spend a weapon focus on them, which works well with the demonic form spells. Additionally, as the demon levels up all of its natural attacks become primary at full STR and BAB. Probably worth taking as a Half-Orc with the feat that grants a bite (Razortusk, I think?), a kitsune, or a motherless tiefling.
Alternatively, Demon can also get the highest spell DCs if you prefer full caster. Battle Oracle (maybe with fire element for second mystery for eventual free empower on fire spells) would allow you to be a powerful gish without having to multiclass.
Magus (particularly Eldritch Scion) should work really well for a demon. Taking a second bloodline should allow you to get dragon for AC and abyssal for +6 STR without having to multiclass.
If you prefer arcane magic, you can build a pretty strong 18th level caster by going Sorcerer 6/Dragon Disciple 4/EK 10 but I think that's better for a Lich than a Demon.
Lich really supports anything. It's best for full arcane casters with a merged spellbook, but has lots of Lich powers which would also be good for gishes, pure martials and even one that is useful for Kineticists. The Lich exclusive spells are all very strong and even non-arcane casters will get decent mileage from them while only using the basic mythic spellbook.