One consideration I would guess creeps into the minds of most of us older adoptive parents goes something like this: Will my kids be embarrassed about having a geezer for a mom (or dad) when they're teens?

I'm thinking the answer to this question will always be ... well, yes.
The good news is that every teen is embarrassed by their parents, and every teen thinks their parents are geezers, even if said parents are... what? ... like thirty-five? Yeah. Thirty-five. (That's how old my mom was when I was 15, and MAN! was she ever ancient in my eyes.)
The bad news is that our kids' friends are likely to have parents younger than we are, a fact that will only serve to emphasize our geezerness. Since there's not a darned thing we can do about being older, short of biting the dust, we have to work with what we have. Thankfully, that includes, in addition to graying hair and crows feet, some wonderful life experiences and a touch of wisdom.
Unfortunately, those won't count for a whole heck of a lot when you pop out of a shop at the mall and introduce yourself to the gang that's collected around your kid while you were inside trying to find a jacket that will keep them toasty over the long winter. There are, however, ways to minimize the mortification your children will suffer every time you appear on the scene.
First, try very hard to act your age. This does not mean that you shuffle about with a walker and take up canasta, but rather that you don't try to pull off a
'tude more befitting one of the boyz in the hood than a parental unit.
Second, don't speak unless spoken to. Yeah, yeah ... that's supposed to be an admonishment for a child, but the less you say in the presence of teenagers, the less likely you will be to say something embarrassing, and the cooler you will be assumed to be.
Third, respect your child. A teen is about as close to being a person as can be, although there are still manifestations of the monstrous immature larval being that is the human child between the ages of 9 and 13. Upon reaching real teen-dom, certain parental behaviors will be interpreted as vicious attempts to humiliate. Acts such as tidying hair in public or wiping dirt from a face with a saliva-dampened finger will NOT be appreciated.
Fourth, respect yourself. Be comfortable with who you are, and with your role. You are parent, child is child ... albeit a teenage child ... and although there are many ways to have fun together, share interests, learn from each other, and so on, this is the kid's turn to be young. That it doesn't last long is something we know too well, so letting them have their go on the wheel is only fair.

As an extreme example of what not to do that would embarrass your teens and have them avoiding public appearances with you anywhere in the same hemisphere ... and with good reason ... note the photos. 'Nuff said.