Will Houdini 9.1 work with an ATI Radeon™ HD 3400 card?

What about the other HD 3000 cards?

The hardware generally isn't the problem with ATI cards - it's the OpenGL driver. It has a history of being somewhat substandard (at least for the non-pro cards), and so graphic artifacts may be seen.

The 3400 won't win any performance awards, but I suspect if Houdini runs on a higher level ATI card (38xx), it'll probably run on the 3400 too. However, it may be sluggish with larger models.

I heard the nVidia GeForce 8 cards also have big driver problems under Linux but I want to have a newer card. I don't need a great performance at home, I have that already in my company. I just can't live with viewport and UI artifacts.

The GEForce 9600 is a really excellent performer for the price (around $160). It's around 75% of the performance of the much-more expensive 8800GTX. Alternatively, you can pick up an 8600 for pretty cheap these days, around $100 (but the $/value is much, much lower).

I'm using the nVidia 100.14.19 drivers with an 8800GTS on Linux (with Debian), they're rock solid.

I'd recommend the ATI 38xx series if I was more confident in their OpenGL driver (especially on Linux). Alas, it's a bit of a no-go right now.