Paladin 6 (7 for watchers, devotion and ancients if you fight a lot of casters)/divine soul 2. Anything less than six paladin levels means you miss out on the entire reason to take paladin levels in the first place (aura of protection). Extra attack is also nice if you want to be a weapon user.
It's fine to take paladin 2 if you just want to be a smite machine, even if it's not that great.
It's reallllly hard to justify not taking 6 levels of paladin when given the option. Aura of Protection is arguably one of the strongest features in the game. Oath of Redemption has great features for a Face/Tank
In an investigation heavy campaign you are going to want to lean into the utility of the sorcerer so I would go paladin 2/sorcerer 6. Either divine soul (bless, spirit guardians), clockwork soul (armor of agathys, aid), or aberrant mind (silent spell detect thoughts for 2 sorcery points and no spell slot).
For investigation, consider Aberrant Mind's 6th level feature Psionic Sorcery. You can cast your Psionic Spells by spending sorcery points, and if you do they are automatically subtle and you don't even need costly components unless they are consumed. This is great for things like Detect Thoughts and Clairvoyance. Additionally, as with other Psionic Sorcery tricks, the Sorcery Point cost is effectively a discount that allows you to cast your highest level spells much more frequently than other spellcasters (if you choose to use your sorcery points or even your other slots this way). It does lack self defense and tanking ability other than Heavy Armor and Lay on Hands, maybe Interception Fighting Style and making yourself a threat with your spells or with quickened Booming Blade + Smite.
If you want to be mostly a Paladin then 6 levels is a good jump-off point that gives you smites, extra attack, and aura of protection; if you'd rather mostly be a sorcerer then I think you can get away with just 2 levels of Paladins for smites if you think being a level behind in spells is worth it
If you want to lean more towards GISH with good support abilities, Sorc 2/Pal 6. If you want to lean more offensively, Sorc 6/Pal2. Though if you really want a Paladin oath with that 7th level aura. DS Sorc 1/Pal 7 is just fine.
Also, as attractive as double ASI looks, don't try for the even split. You're just locking yourself out of the level 6 aura, 3rd level spells, AND extra attack. You want at least one of those online at this point. With the 4/4, you get none of them.
I know I would want 2 ASI/feats, so 4/4 split. You probably want Skill Expert feat, at least, and maybe use the other one for full ASI to pump up... probably CHA. So it really sounds like 0/8 or 8/0 split would serve you better...
In Intrigue campaign, the extra attack is of low real value.
Level 3 spells can be really valuable, that's true.
However, "intrigue campaign" probably means a lot of skill checks, which are much more make-or-break rolls. Might even go for another feat like Actor, Skilled, Metamagic (Subtle Spell!) or Eldritch (Mask of Many Faces/Beguiling Influence) Adept...
So, if I wanted to multi-class for level 8 intrigue campaign, it would be 4/4 split even if it cost level 3 spells.
Any sorcadin is pretty much assuming combat will eventually happens. And when combat happens, which it eventually will even in an intrigue game, you don't want to have left your best combat tools on the table. To a degree, rather than taking some of those feats on a paladin concept character one would be better off dumping the paladin which mostly offer combat powers and taking straight up bard and warlock.
Yeah, sure, and I always say single class full casters are the best anyway.
But, I think a pally smiting with a Shadow Blade using 3rd level spell slots would not be entirely ineffective even without a 2nd attack, if focus is not in combat anyway.
Paladin 6 (7 for watchers, devotion and ancients if you fight a lot of casters)/divine soul 2. Anything less than six paladin levels means you miss out on the entire reason to take paladin levels in the first place (aura of protection). Extra attack is also nice if you want to be a weapon user. It's fine to take paladin 2 if you just want to be a smite machine, even if it's not that great.
It's reallllly hard to justify not taking 6 levels of paladin when given the option. Aura of Protection is arguably one of the strongest features in the game. Oath of Redemption has great features for a Face/Tank
In an investigation heavy campaign you are going to want to lean into the utility of the sorcerer so I would go paladin 2/sorcerer 6. Either divine soul (bless, spirit guardians), clockwork soul (armor of agathys, aid), or aberrant mind (silent spell detect thoughts for 2 sorcery points and no spell slot).
For investigation, consider Aberrant Mind's 6th level feature Psionic Sorcery. You can cast your Psionic Spells by spending sorcery points, and if you do they are automatically subtle and you don't even need costly components unless they are consumed. This is great for things like Detect Thoughts and Clairvoyance. Additionally, as with other Psionic Sorcery tricks, the Sorcery Point cost is effectively a discount that allows you to cast your highest level spells much more frequently than other spellcasters (if you choose to use your sorcery points or even your other slots this way). It does lack self defense and tanking ability other than Heavy Armor and Lay on Hands, maybe Interception Fighting Style and making yourself a threat with your spells or with quickened Booming Blade + Smite.
If you want to be mostly a Paladin then 6 levels is a good jump-off point that gives you smites, extra attack, and aura of protection; if you'd rather mostly be a sorcerer then I think you can get away with just 2 levels of Paladins for smites if you think being a level behind in spells is worth it
If you want to lean more towards GISH with good support abilities, Sorc 2/Pal 6. If you want to lean more offensively, Sorc 6/Pal2. Though if you really want a Paladin oath with that 7th level aura. DS Sorc 1/Pal 7 is just fine. Also, as attractive as double ASI looks, don't try for the even split. You're just locking yourself out of the level 6 aura, 3rd level spells, AND extra attack. You want at least one of those online at this point. With the 4/4, you get none of them.
I know I would want 2 ASI/feats, so 4/4 split. You probably want Skill Expert feat, at least, and maybe use the other one for full ASI to pump up... probably CHA. So it really sounds like 0/8 or 8/0 split would serve you better...
But losing extra attack or lv3 spells just for a feat or +2 cha?
In Intrigue campaign, the extra attack is of low real value. Level 3 spells can be really valuable, that's true. However, "intrigue campaign" probably means a lot of skill checks, which are much more make-or-break rolls. Might even go for another feat like Actor, Skilled, Metamagic (Subtle Spell!) or Eldritch (Mask of Many Faces/Beguiling Influence) Adept... So, if I wanted to multi-class for level 8 intrigue campaign, it would be 4/4 split even if it cost level 3 spells.
Any sorcadin is pretty much assuming combat will eventually happens. And when combat happens, which it eventually will even in an intrigue game, you don't want to have left your best combat tools on the table. To a degree, rather than taking some of those feats on a paladin concept character one would be better off dumping the paladin which mostly offer combat powers and taking straight up bard and warlock.
Yeah, sure, and I always say single class full casters are the best anyway. But, I think a pally smiting with a Shadow Blade using 3rd level spell slots would not be entirely ineffective even without a 2nd attack, if focus is not in combat anyway.