DP from card to monitor is the best option because it's by far the most versatile, it supports just about every (commercially available) resolution and feature. Passing audio is something of a grey area, but if you're talking display signals only... DP works and supports everything.
DVI and HDMI offer identical image quality, and usually adaptors work fine to convert connectors, but there are an almost endless list of random constraints and it can get very complicated. I'll give you a few examples to illustrate the point...
- Converting from or to DVI (whether HDMI or DP) work perfectly as long as it's only single link DVI required (basically nothing above 1200P @ 60hz).
- HDMI has various limits on refresh rate and resolution, and this changes for HDMI 1.4 or 2.0... adapters, cards and monitors need to support the right version of HDMI if you want these higher bit rate signals
- AMD cards only support a limited amount of monitors via passive adapters before requiring native DP monitor or more expensive "active" adapters.
So, all else being equal, get DP monitors if you can.
But, if DP monitors are more expensive and you're only looking at cheap monitors that run 1080P @ 60hz, it normally won't matter as everything supports this.
Finally, if you are getting a high resolution and/or high frame rate monitor, but are looking at cheaper/older models that don't have DP, post back with the specific units you're looking at to get some targetted advice... because in those cases you can't just trust that adapters will work.
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