One way to extend your budget is to purchase fairly new but used amplification. For half your budget you would do well. Many great integrated amplifiers can be found for ~$5K.
Search the forum for streaming options. You might start out with a budget streamer like the Bluesound Node to get comfortable with streaming. Then purchase a better outboard DAC or all-in-one streamer/DAC after exploring the market.
So many ways to go, so little time :-).