Number one is feel. How heavy is it? Can I have this hanging from my shoulder for 3-5 hours? Is the neck comfortable? Is the body ergonomics good? Etc. I don't want to feel like I was run over by a truck after a gig just because my guitar was uncomfortable.
Second is tone. I often play with a bit of crunch in my tone so I want to make sure the bass has a tone that sounds good with my amp and has a good amount of sustain. I don't usually like active basses because I hate batteries and given my tendency to fiddle with my amp settings, I don't want another preamp that I have to play with and be distracted by.
3rd is looks. I tend to be drawn to guitars that look unique. I love Warwick shapes, the Rickenbacker shape, even the Danelectro Longhorn is something I love. If it's something with a unique color, shape, or style, I'm probably gonna be drawn to it.
As long as those needs are met, I'm not too concerned with construction (as long as it's not held together with duct tape), brand, or electronics.