Hi!
There is no definitive answer for your question. Both can be very good, depending on what you want to do/how you want to play your Bloodmage.
In general a Bloodmage - like all Wizards - can be great as a single class character. They get fantastic spells at the highest Power Levels (which multiclassed Bloodmages won't get) - and they advance through their Power Levels/spell tiers faster than a multiclass and get better scaling for their spells.
This is most advantageous if you want to play a traditional Wizard role: sling powerful spells all day long.
However, if you want to play a Bloodmage a bit differently, for example play one who also can do good stuff in melee combat or who can heal party members or is good with ranged weapons and so on, then multiclassing might be better.
Even when focusing on spellcasting a multiclass can be great. One example is Assassin(Rogue)/Bloodmage. Even if you don't plan on using weapons at all: the Assassin gets +25 accuracy and increased penetration as well as increased crit damage for all his offensive actions if he's stealthed or invisible. This also applies to his spells. This can be a valid reason to go that multiclass route - even if it means that you lose access to the high level spells.
Livegiver(Cat form)/Bloodmage is also a popular spellcaster. You combine your healing spells with Blood Sacrifice and use the Cat form (and Cat Flurry) to cast spells incredibly fast.
Then there's also some potent synergies between certain (subclass) abilities: for example Fighter's Unbending + Bloodmage's Wall of Draining makes you basically unkillable. Same as Barring Death's Door (Priest) + Wall of Draining, which makes you truly unkillable. Rogue's Escape gives you +50 deflection for a very short time. But if combined with Wall of Draining it stays for a very long time instead...
So I would suggest you specify how you envision your Bloodmage to function, then we can give better advice.
If you just like the classic Wizard feeling then single class Bloodmage is great. The last two spell tiers are awesome.
That also depends on the specific role/how you want to play him.
A backline spellcaster can relatively safely drop CON* and RES. Profits from high INT, DEX and PER. High MIG, too - if damaging spells are a priority. If the focus is on debuffing/CC then high MIG is not needed.
*Don't drop CON all the way as a single class Bloodmage. You rely on your health to regain spell uses (Blood Sacrifice). It's beneficial to have a robust health pool if want to draw from it frequently and have no constant source of healing.
Again depends. But a generally goodthing is to use arquebus. There's a soulbound one which can be bound to wizards. And it can give your spells a 10% corrosive lash - a multiplicative damage bonus. It also heals on hits occasionally which is nice for a Bloodmage.
Essential Phantom (wizard summon spell) copies your weapons. So it's possible to have a phantom running around with your arquebus, shooting enemies. Since the phantom doesn't cast spells you might want to get the Red Hand arquebus (best arquebus for DPS) and hold it while you summon the phantom. Then the phantom will have it, too - and use it on enemies. Then you can switch to the soulbound one I mentioned before.
Must-have equipment... there's too much stuff that is great for all kinds of approaches. But in general for a single class Wizard getting Rekvu's Fractured Casque (helmet) + Grimoire of Vaporous Wizardry is a top choice. You will get +1 spell uses for each spell tier. But you will get interrupted every time you take damage - which is super bad. Fortunately the helmet makes you completely immune to interrupts as long as you have an injury. It is very easy to cause yourself a harmless injury: cast Necrotic Lance on yourself out of combat until you drop, done: very minor injury, immunity against all interrupts and lots of extra spells.
The rest doesn't matter too much and also changes throughout the game. A Bloodmage might profit well from +max. health gear (mostly amulet) and health regeneration gear (rings, belts and/or armor). Also bonus INT, PER and DEX items alre always welcome.
If you specify how your wizard is supposed to play there can be more specific recommendations for gear I think.
Cheers!