How important is the tonearm?

Very. SME, in my opinion makes the best arms, but pricey. However setup support is excellent. Overall I am a fan of VPI, in terms of sound delivered, value and support it is hard to beat. The dealers are very knowledgeable and Harry goes the extra length to support his products. Great efforts are made to integrate the arm,table and cartridge at the factory, providing less hassle that you get with other arms when trying to marry them to other tables. It leaves you more time to enjoy the music, and not be fussy with the gear.

A question worth to think about, there are differences in Design (not every Arm is done perfect), the ability to guide a cartridge, to handle the resonances coming from the cartridge, the quality of the internal cable, the quality of the bearing, the material from the Armtube (wood, composite, Aluminum ...).

The better your System is (has nothing to do with price) the more you will hear the differences. The main problem is the table (and the connected electronics). Most are nothing special in vibration control and based on this, most think, the cartridge or the Arm has to be replaced when they don't "like" something in the listening..
Next is the Phonostage, most can only do 100 Ω because that is easy to design and with such a damping the higher frequencies are dead anyway.

When you have absolutely no idea from anything, go for a Graham Phantom Arm, it is clever made, works with very much cartridges on a superior level and you can concentrate the later upgrade bugs to other objects.

When I upgraded tonearm from Rega RB250 to Kuzma Stogi Reference I heard a substantial sound improvement. When I replaced Benz ACE H with Benz LP the same happened. Now I am waiting Benz Lukaschek PP-1 to replace Pro-ject Phono Box SE II. I am expecting sound improvement again.

I don't disagree at all that it is the cartridge that is the main focus in getting the music from the grooves. In the context of this thread, however, the device that is responsible for allowing the cartridge to work the best it possibly can is the arm. I have never seen or heard a cartridge work without an arm of some sort. (Those little VW microbus toys don't count!)

Obvisouly, we're leaving out every other link in the chain from cart to speaker, but why cloud the issue when the question here is about the arm.

I prefer the Triplanar to Graham because of the PITA of adjusting the damping fluid on a Graham to get it to sound it's best. The Triplanar is much easier and faster to get set, i.e. it is more user friendly IMO. Still, Graham arms are excellent. The Talea outperforms both of these right out of the box, is the easiest of all three to setup, and will allow one to really hear what a cartridge can do.

SME?!?! Give me a break.

With respect and deference to all the learned responses above, I think it's safe to say that, like everything else in our hobby, ultimately it is synergy that will yield the best results.

A top-shelf arm with a low end cart or a low-end arm paired with a top-shelf cart will both probably be bettered by a mid-grade arm and a mid-grade cart whose mass and compliance are optimally mated.

So neither the arm nor the cart can claim top billing!