One of my favorite places is run by a man and his wife and their adult daughter and son in law. Based on watching Rick Bayless, I’d say they serve what Rick refers to as standard Mexico City street fare.
Beautiful, gracious people, always so hospitable, and their google reviews show it - 4.9 with almost a thousand reviews. The few negative reviews are quite evidently idiots, by the way.
My favorite review was fairly lengthy and glowing but the main point was, “If you don’t like this place, go into the bathroom and take a look in the mirror. You’re staring at the problem.”
They only seat about 20 people but do a huge take out business. Their tacos are always doubled small soft corn tortillas, filled with any protein you want (including offal, lingua, chorizo, pork chunks, el pastor, whatever) and they have a small condiments bar with little cups so you can try any of their 20 or so sauces. I think they do have flour tortillas too, but you’d have to specify as they otherwise assume soft corn. Their tortas are also really killer.
I guess coincidentally, my other favorite taco joint is dad/mom, adult daughter and her husband, and same story about how super nice they are. They undercharge for their food, in my opinion. Besides a great taco lunch (3 tacos plus rice/beans) for $6, their fajitas lunch is just at $8 for beef or chicken. They have on their menus the full choice set between flour, soft corn, crispy corn tortillas. Plus a big sauces bar, too. I may have mentioned this place elsewhere here at HO - I asked the dad owner why his prices were so low and he said it was because so many of the immigrant laborers eat there he wanted to keep the prices to what they could afford. I generally tip this place at 100% if eating alone and at least 50% if I’ve got the kids with me.
The other big contingent here is Cuban style tacos, lots of mediocre Mahi-Mahi tacos but a few places have some really great lobster tacos, invariably on flour tortillas. No idea if these are “authentic” or just an American adaption. And a lot of Cuban-style pork chunks tacos that are fun and tasty. Again almost always flour tortillas.
Oh, to answer the rest of OP’s questions - rare/never beans, cheese or lettuce are seldom too. That’s in the restaurants. When I cook beef, pork, or shrimp tacos myself, we often add thin sliced avocados, shredded lettuce, cheese and the like. Except when I cook the pork carnitas - then I only serve it with a lime wedge for drizzling and some pickled onions.