I searched for the real-deal classic margarita recipe about 25 years ago, until I ran into a bar tender who knew his stuff and was willing to share. This is my drink, and I've not found anything better in all that time.
1 (2 oz) fat, juicy fresh lime squeezed, pulp included
1oz triple sec
3oz 100 percent blanco tequila
Combine in shaker with ice, shake well, and strain into (kosher) salt-rimmed glass. No ice in the glass as it dilutes the drink, or one small cube if you must.
These are tart. I had one girlfriend who couldn't take the tartness and I had to make a sugar syrup for her, but then it's no longer a classic margarita. A splash of OJ is a better way to smooth it out, but wasn't enough for her.
I typically use Espolon for margaritas, but you can certainly upgrade if you think it's worth it or have money to spend. I would never buy Patron or Cuervo as they're both overpriced consumer brands that actually aren't very good. Heradura is good and a widely available alternative.
My all-time favorite is El Tesoro, but it's almost too good to mix and I save it for sipping. Upgrading to Grand Mariner or Contreau instead of triple sec is great for special occasions, but wasted if you don't also use top shelf tequila. So I have my every day mix and my very special occasion mix, but the 1-2-3 formula never changes.
If you try to order one of these in a restaurant bar, good luck. They will either use a mix or Roses sweetened lime juice, and both are a waste of good tequila. Better to sip straight tequila or get a lime-mixto-slushy like the Mexican places make by the gallons.
If you ever can find or order a bottle of El Tesoro Blanco, don't pass up the opportunity. You'll never be satisfied with Patron or Cuervo again.