best place to connect with relative in Oaxaca airport?

The Oaxaca airport is quite small - ie a single terminal with only a few gates. Shouldn't be an issue just waiting for your friend and then proceeding to customs together.
You'll be passing thru customs in Oaxaca too - not in Mexico City.

It is indeed quite small, we were there this summer. You will already be through immigration in Mexico City (and from our friends we met in Oaxaca who go through Mexico City, Mexico City airport is a zoo for connecting). She will have to go through immigration first. This airport is so small that i would suggest that you make yourself comfortable in the outer area after the customs line, and scope out getting the fixed-rate (and dirt-cheap) official cab into the city center. Seriously, if you are in that area she cannot miss you after she clears all checkpoints and enters there. And there is more than enough English there. There is really no place to wait in the customs area.

Per Larry, it sounds like the arrival procedure has changed since our last trip a few years ago, so waiting on the other side of the customs line is the way to go.
Per his suggestion, ensure that you book your cab from the official, licensed, taxi rank in front of the terminal. There are likely to be a few touts running around trying to lure you to one of their vehicles at a "special set price". Don't fall for it.
And he's right - the Mexico City airport is a real zoo.

Thank you Robert and Larry. Your responses are really helpful!

Just to agree with Robert and Larry -- it's a small airport with things close together. You can't get lost and the easiest thing would be to wait for your friend after customs outside security. Get a Spanish phrasebook and learn a few basics.

You and your friend should know that bags will pass through a metal detector after you land (looking for guns and such), and each person pushes a big button that triggers either a red or a green light, most often green. If red, they'll open the bag and briefly look through. If green, no bag opening. This button process is to randomize the searches. It's no big deal, and the inspectors will know enough English for basic communication.

Thank you, Dick. I appreciate the intel.

I'll just echo all the above and add this: relax, dial-down your stress, and enjoy your visit, you will be perfectly fine. There is so much pervasive, collective hysteria about safety in Mexico, it can really freak out people who are otherwise quite rational. Use common sense, and you will be safe and sound. Just as you would in Europe (or at home) stay out of sketchy places and neighborhoods (especially after hours), don't go looking for trouble, trust your gut but use your head, and you will be fine.

Yes to the above about cabs: don't hail a cab on the street (or at the airport). Get an official cab from the obvious, easy-to-find cab counter (aka "sitio") at the airport. If you need a cab elsewhere, ask your hotel or restaurant to call one for you, rather than jumping in some random one driving by. In major tourist areas, most people you will need to deal with will speak enough English to get by; use as much Spanish as you can, at a minimum learn "the polite" words to show respect (same as in any city anywhere).

You can do this. It'll be fine. Have fun!!!

Thank you for the reassurance. I picked up a pocket phrasebook today.

I affirm what David says about trying hard to dial down anxiety, I rendezvoused with my friend at airport in Cancun and we took a bus to merida...
The only encounter we had in nine days that felt spooky was with a European hotel owner who accused us of loitering in front of his property.
The locals were lovely and helpful.