I did a step-parent adoption and TPR this year (my husband adopted my kids). The first and formost thing we felt important was that the children were ok with it. At 9 and 6 they might not understand completely(heck some of us never understand how a parent can give up their children because of money) but then again they may understand more then you realize. Part of the reason we did it was due to the legalities. We wanted to assure that if somethign were to happen to myself that the children didn't lose their mom, their home, school, friends(we live far away from any other family), and the only person that's treated them as if he was their dad. My kids are 11 and 13 and it's done well.
As far as the contact thing I totally understand where you coming from. The question however is though, how much contact does bio-dad have now? If he has any or even half way frequent contact it will definately be harder for the kids to understand if you cut off all contact. In my case the last contact bio had with children was April of 2002(initiated by myself) and before that it was July of 2001. By some sort of miricle (yeah right) the state found him and got him served for the $24,000 in arrears he owed the month following the finalization of the adoption. Per his MO he contacted by mail less then a month after a wage withholding was taken out. It was birthday cards to my youngest son, a month late. I got them, and we did show and tell the children. I did tell the older that if he gets cards next month(which I'm not counting on) that we would show him also but that the ones we received, and anything else in the future if there is anything would be saved but not shown to them. We explained that they need to concentrate on being children, their school and their activities and friends and not worry how long this man was going to hang around this time then worry what they did when he took off again. One son handled it well. With the other one you could see the excitement that his 'daddy' had contacted even though he was the one who really wanted the adoption done. This was about 3 weeks ago and we're already back to normal. I considered contacting bio and telling him that no contact would be accepted but that feeds into him so as I said we promised to save the things and when they are 18 or ask for if there was anything they would see the things.
BTW... as stated if you don't 'forgive' the arrears they are always owed. In my case the support went from $113 owed a week to $30 a week paid toward arrears.
Something I've come to learn and accept is that although there is an adoption it never erases biology and your children will be left with the question as to how a parent can simply 'give them up'. I tell my children that I can't answer that question for them and that once they are older and try to speak with their bio he would have to answer that. I've also prepared them for the lies that will be told to them and keep my documentation to counter those lies, it's always helped me by showing my kids reality.
Good luck!