I will answer with a personal experience.
First, meet in a public place, do not give your home address! And meet at a reasonable time.
I met for dinner and my immediate impression was...he is nice. He was very attentive, and appeared to be very interested in getting to know me. But the more we talked, the more this little voice in my head started telling me to put on the brakes. Everything I said that I would like to do, he wanted to do with me. When I mentioned that Sunday's were important to me. That they were my family day, he said that's ok as long as I'm with you when you spend it with your family. This red light went off in my brain. Whoa wait, first date and he's telling me that from now on, everything I do, he will be with me? How controlling and suffocating is this guy? He started making plans for my life then and there...again first date. I finally got out of there and thank goodness for caller id - never answered his calls, never returned them.
Another sign...my dog loves everyone. She thinks everyone comes to my house to see her, not me. Everyone is her best friend. Except one guy I had pick me up. I heard her growl for the first time in the two years that she had been in my life. She growled, she barked, she stood between us. And since I firmly believe she came in to my life at a time I needed a best friend and that God brought her to me, I listened. I showed the guy the door, told him I wasn't going and locked it behind him. Crazy thing to do but not one I regret.
Look for someone who is interested but not controlling. Someone who suggests a next date, not makes plans for the next date. Listen to your inner voice and trust your instincts. Watch how much they drink and if that person does drink, watch if there are any changes to their personality. And stay sober yourself! And if your dog or cat behave unusually, show them the door!