As young as your picture looks, you can probably afford to be picky for a long time. If you were 50 and wanted to be married and had for decades, I'd probably say you shouldn't be too picky.

Also, if you are meeting women on the Internet, you may be able to afford to be extremely picky.
Someone I know this past week was corresponding with a woman trying to get an annulment, she said, in the Philippines, from a man who'd left her for another woman 6 years ago. She said she needed $5,000 to get the annulment. It sounded like a scam to me. I don't know why he'd want to mess with a situation like that anyway.
Assuming you don't have kids and you are as young as you look, if I were you, I'd stay away from marrying a woman with kids unless God really spoke to me somehow to the contrary. In parts of Asia, if that is the pond you are fishing in, there are plenty of young virgin women who don't have a lot of baggage. The cross cultural issues are enough without any baggage. You don't want the father of the kids in the picture later in your life if you can help it.
These were some guiding verses for me in finding a spouse.
Matthew 5:32
But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery.
and
I Corinthians 7
10 And unto the married I command, yet not I, but the Lord, Let not the wife depart from her husband:
11 But and if she depart, let her remain unmarried or be reconciled to her husband: and let not the husband put away his wife
If you want to marry a widow with kids, that's not a sin. If God leads you to that that's fine. If you don't have experience being a parent, though, it may not be the best situation. You also don't have the other father issues to worry about if you marry a widow. There may also be some godly single mothers out there who never married. But I don't think it's wrong to have a preference for someone who doesn't have children already, especially if you are young. I don't know who the Lord will lead you to, but I found when I asked the Lord to lead me to the right person, He did.
Too picky would be if the Lord put someone in your life to marry and you were too critical to marry that person.
I went the route of not marrying until I sensed the Lord directing me to do so. Of course, I prayed about it. When I met my wife, I sensed something was going on after our simple, friendly conversation. I went home asking if she was supposed to be my wife. My wife went home after that conversation praying about marrying me.
If you aren't in a state in life where you can support yourself somehow or you aren't close to being there yet, you shouldn't consider finding a wife to be an urgent matter yet.