Advice needed: am I going in the right direction?

I'm new to hi-fi sound world and spontaneously bought myself Yamaha NS BP200 passive speakers and Onkyo A-9030 amplifier, because I thought that connecting it to a PC will be a piece of cake - just buy some external sound card and you are good to go!

However after doing some research I found out that it's not that simple and now I'm kinda lost: does it (PC -> DAC or sound card -> amp -> speakers) even work like this. So, my question is:

Am I going in the right direction? And if yes, maybe you can suggest some DAC/external USB sound card that could suit my case (budget is about $150)?

@big greg.
Your system will dictate the level of sensitivity you require.
In your case, I would suggest a Schiit Bifrost Multibit.
Given your wishing to use a recording device, buy the Steinberg and see if it satisfies in your system. Seem to me it is very full function at it's price, not designed only as a  DAC. I would think a simple USB DAC would sound better for home audio.

Thanks for the replies, you really helped me a lot. So, an extenral DAC is a way to go, but in some time I will also buy the Steinberg sound card, it would be interesting to compare them. If someone needs an amateur opinion on a difference between $100 DAC and sound card of the same price, write me a message, and I will share my experience :)
You are welcome. Let us know what you purchase. I am following a bid on a HRT Music Streamer II on E-bay. Now it is under $20 (+$7 shipping).  Great way to bring computer audio to a budget system.