I usually do a right card/wrong card trick. They pick a card, return it, I find the wrong card and place it in their hand. Then it turns into theirs.
The reasons I start with this trick are:
1. There's no setup.
2. It gets good reactions as it's a fairly magical effect
3. There's very little sleight of hand so it's easy for me to do without screwing it up
4. It's simple and plays out fairly quickly. Generally I don't want to open with a trick that takes awhile to get to a climax. If they're interested in seeing more I'll do something with a bit more process.
I used to do ambitious card a lot but occasionally people would just sort of stop paying attention after the first phase of the card coming to the top, even though there's 2-3 phases after that that are arguably stronger than the first. Like they seemed to think that was the end of the trick and I always felt awkward going "Wait there's more" like Billy Mays.
Also, just out of curiosity, what is the ambidextrous card trick?