As a person looking for someone on a dating site, be very clear in your mind and heart what your must-haves--and especially what your must-not haves--are. Then be flexible. Yes, that’s contradictory, but maybe you want someone without kids, but s/he turns out to match all the rest of your must and must-not haves. Is it an insurmountable issue? Only you can answer.
All of this applies to dating when you meet off-line--in the real world. Be transparent, think out loud, and so on. If your goal is to have an emotionally connected relationship, then behave that way from the get-go.
Keep in mind that people are “selling” in the beginning of a relationship. You’re seeing their best behavior, physically and emotionally. Additionally, when people begin dating and like each other, the brain begins to be flooded with happy hormones that wear off within 24 months. During these early months, people may be unaware of or in denial about red flags. Pay attention! Trust yourself if red or pink flags pop up.
Most people go from one relationship to the next with their same behaviors (unless you do the hard work on yourself to change). You may have noticed that you keep running into the same issues with people. Look at yourself first.
All of this is why therapists recommend waiting at least two years to get engaged.