... personal experience of me, works, but is more'n a little awkward.
Me, I'd ditch 'em all.
My advice is based on the personal experience my wife and I have had ... yadda yadda yadda
I agree with that. And why's "experience of me" awkward?
Well, more idiomatic would be: "experience of mine". It's the much debated double possessive. And here's your problem:
1. a) "I offer practical advice based on personal experience of mine."
1. b) "I offer practical advice based on personal experience of me."
b) is correct enough, but I prefer a). There's no contest, as far as I'm concerned.
2. a) "I offer practical advice based on personal experience of my wife's."
2. b) "I offer practical advice based on personal experience of my wife."
Here, my judgement's less clear. I think I might lean towards the second in writing, myself, but reading I wouldn't think twice about either.
Now, if you co-ordinate both you run into trouble.
3. a) "I offer practical advice based on personal experience of my wife's and mine."
This sounds fine to me, but some people might not like the ambiguity inherent in this. Are the experiences separate (your wife made her experiences and you made yours), or are the experiences something you share? Personally, I'd think context takes care of the ambiguity, so it's no big deal. (If it's marriage advice, I'd assume it's experience together, for example.)
Of course, English has a way to stress that you're talking about a unit: "of George and his wife's". See? Only the last item gets the possessive 's, and it's clear what comes before is a unit.
However, you run into a problem with the nasty pronouns, which have irregular possessives. What you end up with is:
3.b) "I offer practical advice based on personal experience of my wife and mine."
Um, no. This sounds distinctly odd. It doesn't look like the [wife + I]'s version. Rather it looks like you're using a single genitive for the wife, but a double for yourself. Not really. No.
So, what if you treat it as a unit: []'s? Take the genitive out of the pronoun? Move it to the end of the co-ordinated possessors?
3.c) "I offer practical advice based on personal experience of my wife and I's."
There's logic to it, but - um - no, not really.
So, perhaps the best way would be just to do away with the double genitives?
4. a) "I offer practical advice based on personal experience of my wife and me."
Realise how this is the version you've chosen? Of those mentioned, it's probably the best. Even though I'd never say "experience of me" and always "experience of mine", I'd make an exception for the me-version in this special case. Why? I don't like to mix; i.e. using one single genitive and one double genitive:
4. b) "I offer practical advice based on personal experience of my wife and mine."
Not really, no.
See how 4. b) and 3. b) are exactly the same, but arrived at by different reasoning? (To my mind, 4. b) takes precedence when reading; that is, on reading, the 4-b reasoning will always come to me first.)
So, of all the versions here, I'd chose either 4. a) (which you chose in the original post), or 3. a), given that the context does take care of the inherent ambiguity of that sentence. But luckily we're not forced to choose and can re-write the sentence in the way Medievalist has suggested. Best to write around the problem.