Couple things: This is real advice, hope you aren't trolling.
1. Getting close to the kids early on will cause both you and the child to form a really strong bond. Even if pops is in their lives, they are going to form a bond with anybody in their space and spending time with them. You should set those expectations appropriately and not go too hard too fast.
If you don't plan on being there in the long term, you're only setting them up for hurt. If their mother has feelings for you and views you as a good figure in their lives, she may not necessarily see this so it is up to you to create boundaries and set expectations.
2. You have to be honest with yourself and mature quickly if you do decide to pursue this long-term. If it works out, more might be expected of you. If it doesn't work out, don't be one of those guys on that, "damn, this bytch a single mom, I shouldn't have given her the time of day" bitter stuff that a lot of dudes get on.
Just be honest about what you want, where you see yourself, and if they factor into it (and if so, how).
3. LOGOFF THE INTERNET, ESPECIALLY THE COLI, AND LIVE YOUR OWN LIFE. Don't take advice from internet sociopaths who have little to no relationship experience and view everything through an imaginary lens.