Everyone has a theory about a Margarita. Here is mine. Strip it down to it's basic structure - Tequila, orange liqueur and lime juice. No Margarita mix, no orange juice, no swirl. Use quality ingredients and get the balance between sweetener and acid right and you're going to be happy every time.
First, the Tequila. You may think that you can get by with Jose since it will be covered up by the other ingredients. This may be so if you're using a pre-made mix, but in our stripped down version the Tequila will show through. So use a 100% blue agave Tequila. It doesn't have to be Don Julio 1942, just a good blanco or reposado. Sauza Hornitos is a good choice with it's clean agave flavor with just a hint of oak (it is aged in 10,000 liter oak lined tanks). Also Cazadores reposado is another choice.
Things get more sticky with the orange liqueur. You have a lot of choices here and there are strong advocates for each choice. The choices break down into two separate camps, the Triple Sec camp and the Orange Curacao camp. Triple Sec is a cleaner, more highly refined liqueur usually based on a high proof rum distilate. Orange Curacao is a little heavier and is usually based on a brandy distilate.
Examples of Triple Sec include Cointreau, Bols and Combier Triple Sec, Luxardo Triplum, Controy and Patron Citronge. Orange Curacaos include Grand Marnier, Gran Gala, and Marie Brizard and Bols Curacao. I prefer more body in my Margarita so I use Gran Gala. To me, Cointreau and other Triple Secs seem a little thin. But that's just me. The most important thing is to make sure whichever sweetener you choose is in balance with the lime juice in your Margarita.
Salting the rim is optional - it's totally up to you. I like to throw a tiny pinch into the drink to get a little salty flavor to go with the more dominant sweetness, citrus, and fruitiness of the Tequila.
I use rocks glasses usually, but I have Margarita glasses for company. These are thick stemmed glasses with straight sides that you sometimes see in Mexican restaurants.
If you want to use syrup as a sweetener as well as orange liqueur, here is a recipe that incorporates syrup:
1 1/2 oz Tequila
1 oz lime juice
1/2 oz Gran Gala
1/2 oz simple syrup (2:1 strength)
This will yield a slightly sweeter Margarita than the recipe listed above.
Every cocktail book seems to have a theory about the origin of the Margarita. There is no definitive writing on this matter (at least none in my long searching on the subject). There are a lot of claims and stories about who invented this drink. The most convincing one I have seen is on page 108 of Imbibe!: From Absinthe Cocktail to Whiskey Smash.