Here is how I would rank the classes:

1.1. Fighter - Fine in BG1, but afterwards - avoid. Why would anyone play a pure fighter if the Berserker kit is available ?
1.2. Berserker - Good in the original games. Downgraded to great dualclass option in the EEs. The lack of extra damage reduction is just not cutting it. And the rage isnt so special if you're winded afterwards.
1.3. Kensai - Only interesting as dualclass to mage. Maybe thief if you're really into that.
1.4. Wizard Slayer - Avoid. Absolutely the most godawful class in the game.
1.5. Barbarian - Best tank in the original game, still among the best in the EEs. Can chain rage, which is why they stay great.
1.6. Dwarven Defender - I mean they are fine but also kind of boring. Once the Barbarian gets Hardiness they are just as good and they are a hella lot more fun before that, too.

2.1. Ranger - Definitely superior to the bare fighter. In the original games the superior dualclass option to Cleric because they also got Druid spells; by far the nicest access to Druid spells. In the EEs they took that away, but Rangers get real spells which turns them into the elite among the tanks.
2.2. Archer - If you are really into it, knock yourself out.
2.3. Beastmaster - Avoid. Great idea on paper, horrible implementation, sacrifices a lot for hardly any benefit. In the original games if you dualclass them to Cleric they run into the problem that you'll be stuck on the levelup screen because you cannot spent any more weapon points.
2.4. Stalker - Avoid. If you are really into backstab maybe play Fighter/Thief ? Much better deal.

3.1. Paladin - Same as Fighter, got a superior kit in BG2.
3.2. Cavalier - Best Paladin in the EEs, in BG2 unfortunately less so. The disadvantage is at best a mild inconvenience, the benefits are pretty awesome. But only when the EEs fixed the spellcasting Cavalier became one of the best tanks.
3.3. Inquisitor - The best Paladin variant in BG2. The best non-mage magekiller in the game, with True Sight and super strong Dispel Magic. Unfortunately in the EEs the loss of spells really hurt this kit and while they are still awesome magekillers, they are only a second class tank now.
3.4. Undead Hunter - Better than the base class for sure, too, especially in the EEs, but Cavalier has the nicer goodies.
3.5. Blackguard - Avoid. Cant use Carsomyr. And they dont get a sufficient compensation for that. Not even remotely.

4.1. Cleric - Avoid, actually. All original romances are healers, so you dont want to play one yourself. And if you insist - only play as dualclass from Berserker or Ranger. Best healer class, can buff themselves massively to temporarily turn into good fighters. Even more so if they have been dualclassed from Fighter or Ranger.
4.2. Cleric of Lathander etc - Avoid. They all get nice-ish goodies but again, nothing beats the dualclass from Fighter or Ranger.

5.1. Druid - Avoid, for the same reason as Clerics. Also Druids are a great class in many respects - but their XP curve ! Oh so painful. The by far nicest access to Druid spells pre-EEs was a Ranger(n)/Cleric dualclass.
5.2. Todemic Druid - Not really that relevant differences to regular Druid.
5.3. Shapeshifter - Turns temporarily into a pretty decent tank with their self healing.
5.4. Avenger - Clearly the best druid kit.

6.1. Monks - Avoid. A "warrior" class without hitpoints, without protection from critical hits, without percentile strength.

7.1. Shaman - The better druids. Progress like Mage, i.e. quite slow, but without the sudden delays of Druids. Can summon "infinite" animals to help in combat.

8.1. Thief - This class has their fans and I'll leave them to that. To me this is just painfully slow.
8.2. Assassin - Doesnt seem to be a good deal.
8.3. Bounty Hunter - Interesting traps, if you're into that. Of course the best traps are HLAs and even Bards get them.
8.4. Swashbuckler - THE thief class for dualclassing to Mage, after you have accumulated sufficient minimal thievery skills
8.5. Shadowdancer - If you are absolutely into backstab you'll love this class, obviously.

9.1. Bard - Avoid. Its a severely crippled Fighter/Mage that gets gimmicks for all the things they lost.
9.2. Jester, Skald, Blade - Avoid.

10.2. Mage - The only problem is why would you ever play a pure mage and not a Swashbuckler(n)/Mage dualclass ?
10.2. Specialist Mage - The good specializations are Conjurer, Illusionist, and Necromancer. None of them get Edwins amulet though.

11.1. Sorcerer - The strongest spellcaster in the game, but of course you have to accept holes in your spelllist.
11.2. Dragon Disciple - I mean its fine but really the advantages you get are gimmick-y and losing a spell per spell level hurts quite a lot, actually.

Just found out: apparently so many people demanded the bug with Druid spells on a Cleric if its a dualclass from Ranfger (or a Ranger/Cleric multiclass) back that theres a .ini (well now .lua) variable for it !

ROTFL

And since I havent touched the .lua - its definitely set by default, too !

Its definitely by far the nicest access to druid spells that you can have. Clerics may not level as fast as Druids on lower levels, but around level 15 Druids get unbelievably slow. Even worse if its Jaheira or any other Fighter/Druid multiclass, of course.

Interesting assessment. Still, I'm thinking about BG2, single player. Aren't shaman denied any stronghold?

And what if you DID want to do a full playthrough while getting the bard stronghold? I'm curious about what you'd recommend for PC and party in that case?

Okay first things first. I somehow forgot to rate the multiclasses.

General - multiclasses are really stong. They are good at any level and when other classes hit diminishing returns, multiclasses still keep improving. They are one of the features where AD&D shines and later versions never came up with something like this again.

The multiclasses pay for their advantages with low hitpoints, few weapon points, and slow leveling. Also, multiclass Fighters cannot put more than two points into a weapon, while dualclass Fighters can. And you cannot get any advantages from kits - unless you play a Gnome mage, then you get to play an Illusionist.

Fighter/Cleric - I'm not sure where exactly I would put them, but they are definitely in the top 10 of strongest classes. As mentioned before, Clerics can buff themselves to be pretty decent fighters and this multiclass of course really is a fighter, too.
Fighter/Druid - Really the only thing Druids get to directly improve the Fighter is quite late the Ironskins, and thats purely defensive. And Jaheira only works that well in BG1 because she gets a very solid xp advantage over the rest of the party. Still, its not a bad deal. Until you hit about Druid 13 and then its painful.
Fighter/Thief - If you want to have a full thief that still gets more than enough skillpoints to distribute, but that also gets multiple attacks per round, good attack, wide weapon choices (not for backstab though, you have to use weapons useable by pure thieves to get the backstab multiplier), etc, etc etc, here is your deal. Picking Halfling for race seems like a nobrainer here, Dex 19, short race thievery bonuses and short race saving throw bonuses are very hard to argue against. Buf of course Dwarf can have a percentile strength while Halfling cant.
Fighter/Mage - Really just the strongest class in the game.
Ranger/Cleric - I mean there is absolutely no reason to play Fighter/Cleric instead. After all, both can only put up to two points into weapons. Except you can only pick this class as a Half-Elf. Also, the bonuses you get are kind of gimmicky. A bit of stealth, two points in two weapon style for free. Nice. But not really too relevant. Obviously if you play the original or have enabled the bug then you get Druid spells, too, thats quite substantial especially if you dont otherwise have any Druid spells.
Cleric/Thief - So you are both support classes at once ? I know of no good synergy bonus here though. Limited to Cleric weapons, and can only backstab with weapons that thieves can use, so its only possible with Clubs and Quarterstaffs.
Cleric/Mage - The second strongest class in the game, at least in the later game.
Thief/Mage - Can backstab constantly once they learned Mislead. Just like F/T this is a very fun class, and obviously as a Mage theres countless possibilities.
F/C/M - Now this is really slow leveling. And what is this class even supposed to be ?
F/T/M - Actually you can just think of this one as a thief with bonuses. Of course learning stuff like Mislead takes a lot of time. To be precise you need to have 2,250,000 xp until you reach mage level 12, spell level 6, and thus Mislead. If you would force me at gunpoint to recomment a bard, I would go for Skald. Primarily because their song works on summons, too. That multiplies their effectiveness quite nicely.

This was really for all parts of BG1+2 and addons, including the EEs and the Black Pitts minigames, and primarily rating classes on strength.

Yes Shaman is the only new class the EEs introduced and they didnt get a stronghold, because there was no good match among the existing options. Personally I would have given them the sphere. It already doesnt make too much sense that Sorcerers get it, too, not just mages.