How to meet my new partners children?

You just started talking to this man? You hardly even know him. Now is not the right time to meet the children. Children bond quickly to adults. If you two don't last no only will your heart get broken but so will the kids.

Go out on a few days with this man alone. Get to know him. If you two feel the relationship is going somewhere then meet the children.

Good idea on the toy thing, make sure that the children like it, talk about it with the mother. You want the children to like you, gifts should help. Depending on how attached they are or were to their father is also a big factor. If they knew their father well and lost them you may resent you because they might think you are trying to replace their dad. If they never really knew their father then I think you're set. If you aren't that good with kids then do some research on how to get them to like you. You must mean a lot to this girl if she is letting you meet her kids. Try your best to get them to like you, make them laugh and smile, this proves to the girl that you are good with her children, being able to do that is important.

they're so young, so a little gift is a nice gesture.

ya it does