Only use RCA to speaker is the speaker is active (ie, has an amp built into it). The preferred method for best sound quality is to use a quality Class A, Class A/B, or a HIGH END Class D speaker amp and connect to passive speakers using the traditional speaker wire method. If the DAC has more than one digital input it will allow you switch between them. Speakers in that price range are junk. Emotiva and Chane have some low-end speakers that are probably as good as you can get at that price range (beware though Emotiva amps are bad).
$300 will only buy you bad sound quality. It will certainly be better than a $40 Logitech speaker system, but such a system would be strictly lo-fi.