That iBasso D-Zero is $109 plus shipping. You said your budget was $150????
An external sound card is, minimally, a DAC with line out connections. It's mainly just a difference in naming for marketing purposes. You have headphones, so you need a headphone amp, too. That iBasso IS effectively an external sound card with DAC and headphone amp. It has a plug for auxiliary out for your speakers, and a place to plug in your headphones. You could alternatively choose to buy a separate DAC and headphone amp, and then split the signal from the DAC to go to your speakers and the headphone amp. Finding a combined unit that also has a line out/auxiliary out for your speakers would seem more convenient.
So that ART headphone amplifier is just a headphone amp. It still needs a separate DAC to convert the digital to analog. And people here on head-fi don't talk about buying those ART units.
Research some on the portable amp
and the dedicated source
forums. There you'll find people discussing all kinds of components for what you are trying to do.