Arcanist, Sorcerer, and Wizard are three of the most dominatingly-powerful classes in the game
Each of these classes, built right, can do just about anything, and in many cases can do very close to everything. The spell list they have access to is the best in the game, and spellcasting is the best class feature in the game.
These three can nullify a huge array of problems with a standard action. They are all extremely capable of getting new solutions in those cases they run into a problem they cannot already solve.
At very-low levels, these classes have somewhat-low stamina, and their spells are not nearly as dominant as they quickly become, but smart and careful play can ensure statistical advantages in almost every endeavor. As they level up, their stamina and power increases exponentially, and it is not long before they are clearly superior to almost everything else. Around 7th-level, at the latest.
This does, however, rely on careful and creative play. Extremely thorough knowledge of the massive sorcerer/wizard spell list, and what spells are best for which situations, is required. It takes a lot of work and mastery to accomplish. Just as the ceiling for these classes is very high, rock bottom is a very dark and dank bottom indeed. That said, they have exceptional ability to fix any mistakes they make; even if they play very poorly for a long time, they can very suddenly become powerhouses by simply preparing better spells (the sorcerer is, obviously, somewhat worse off in this regard).
Summoner and witch are close
The summoner and witch are very close in power to the three listed above. The eidolon is an incredibly versatile and powerful class feature, summon monster offers a great deal of utility, and the witch is pretty much a lesser wizard.
The summoner has the side-benefit of being much easier; it’s pretty easy (and effective) to hide behind the eidolon. The witch is actually kind of harder, though probably more powerful; the familiar is a massive, glaring vulnerability, and the spell list just isn’t quite what the sor/wiz one is. But then, the witch gets to heal status ailments, which none of these classes get, and though it’s supremely limited, that could be a big deal (see below).
Alchemist, bard, and magus are more well-rounded
These classes are not nearly as powerful as the above, but like the summoner they can be a bit easier, particularly the magus, as they are sturdier before spells come into play. In particular, they also allow for more up-front characters, which is not only something many enjoy, but also is often a useful platform for the more magely casters to put buffs onto.
These classes are reasonably competent, and are in a pretty sweet spot, power-wise. They also add a bit of variety compared to the above (though the summoner’s eidolon does a depressingly good job filling the melee role). A group at this tier, or at this tier with support from the above, will be very competent.
The alchemist is also very important because it is the only class here that gets lesser restoration and restoration, which are otherwise major gaps in the capabilities of arcane spellcasting.
I have no experience with bloodrager, investigator, or skald
Just to be upfront about it: I have no practical experience with these classes, unlike the above. So take the below with a grain of salt.
That said, the bloodrager’s spellcasting is extremely weak, and nerfed rage powers are not a particularly exciting thing to get in return. This class looks like it could be quite fun in a low-power game, but I would not recommend one in a game alongside the above.
Skald looks better; its spellcasting is closer to the bard’s, and it gets enough barbarian powers to be interesting. I actually want to see this class in play at some point. Probably plays well at around the bard tier?
The investigator seems to be on a similar page as the skald, though the existence of the vivisectionist alchemist makes me wonder what the point of it is. I rather like the concept, anyway.
One major thing arcana is lacking: healing things other than HP
HP healing won’t really be a problem; even the bard can handle that well enough with a wand of cure light wounds (though make sure the party does get such a wand somehow), and the witch is actually pretty good at it, but healing status effects, ability damage, and conditions is going to be much harder. The cleric list is pretty much the only places you find really good healing of that sort.
The alchemist and witch are the stars here: the alchemist gets the crucial lesser restoration and restoration spells (though he needs the Infuse Extract discovery to share them), and the witch gets the various remove ailment spells, plus heal at very-high levels. Between them, they cover the major healing options that are otherwise missing from arcane spellcasting. The cleric still has major advantages (not least of which being that the cleric can handle both of these things), but if both of these classes are represented in the party, they can probably handle these things about as well.
If either or both of these classes does not get chosen by players, be aware that anything that inflicts an ongoing status effect is likely to force the party to retreat, to find a temple to get it dealt with. That, or if absolutely forced, to throw themselves into later encounters at a massive disadvantage. Deciding how you want the campaign to play out with this reality would be really important. Items and institutional resources are likely going to be necessary, which means you, as DM, have to make them available.