When I first started with using Amp Sims, I had an old core2duo circa 2005 and realtek HD on the motherboard (circa 2005) audio using the line in.
I used ASIO4ALL and had about 10-15ms latency. The problem at the time was that a background process would kick in and it would cause the audio to pop occasionally. Note that I found in my case that forcing the Realtek drivers to 96k actually lowered my latency. I suspect that chipset was downsampling to 44k/48k.
I used FREE vsthost software ( http://www.hermannseib.com/english/vsthost.htm ) to host the Amp Simulations, and I used FREE simu-analog VST ( http://www.simulanalog.org/guitarsuite.htm ) for decent pedal/amp sims.
So the only thing I had to pay for was a 1/4 inch to 1/8 inch adapter for my (noisy) audio cable I pulled out of the cable snake-pit-box in my closet.
Total price: about 2 bucks
Once I got that all in place and I played around a bit, I then upgraded as possible or where I felt a lack of features.
All this was on a desktop. I tried this on a cheap laptop at the time, but it was not suitable. I expect anything made in the last 3 years is probably going to be satisfactory.
I am currently using a stealthpedal (but not the software) for the midi pedal and sound card features.
The main advantage of using a separate device or add-in card with its own ASIO driver is that you can still use the onboard audio for e.g. youtube or media player(s).
Make sure whatever you choose has a native ASIO Driver.