The best gyros meat is made like they do at a Greek restaurant on an upright (vertical) spit... A big slab of gyros meat slowly turns in front of a heating element and has the strips of meat cut off by the chef with a long slicing knife gradually as the outermost meat browns.
To approximate this at home you can use a spit over a bed of coals on a barbque grill and cook slowly for 30 to 45 minutes. Rotating the spit and slicing thin slices off to make the sandwiches as it browns.
I must admit though, I usually just cook it in the oven at home.
Typically, gyro meat is at least 50% ground lamb and the rest beef. Meat with a fairly high fat content works best. The spices are usually garlic, onion, marjoram, rosemary, salt and black pepper.
When I make it sometimes I use 50/50 lamb and beef ... and sometimes all lamb. Here's the recipe I use for all lamb.
1 pound ground lamb
1/2 cup very finely chopped (or shredded) onion
2 teaspoons fresh minced garlic
1/4 tea garlic powder
1/4 tea onion powder
3/4 teaspoon salt
3/4 teaspoon dried ground marjoram
3/4 teaspoon dried ground rosemary
1/4 teaspoon black pepper
Mix everything together and let sit in the fridge for 2 to 4 hours.
Blend in a food processor for about 1 to 1-1/2 minutes. (When cooked, this will give it a more traditional gyro feel on your palate.)
To bake it, form in a meatloaf shape and bake for about 45 minutes to 1 hour, at 325 degrees F. It should be just a bit dry.
Here's the recipe I use for Olga Bread to use for the sandwich if you want to make the pita bread yourself at home ...
1 cup milk
1/4 cup water -- warm 110-115 degrees
1/4 cup honey
4 cups flour
1 teaspoon salt
1 package dry yeast
1/4 cup margarine
3/4 teaspoon sugar
Scald milk. Place scalded milk in a large bowl with honey, margarine,
salt. Stir until margarine is melted. Let cool.
In a small bowl, combine: sugar, dry yeast and warm water. (proof the yeast).
Add 1-1/2 Cup flour to milk mixture, add egg, and mix well.
Add yeast mixture and 2-1/2 cups flour. Mix until dough is sticky. Knead on a floured board. Place dough in a bowl (oil it first) and cover. Let rise until double in size. Punch down dough and cut into 16 pieces. Form ball with each of the 16 pieces. Roll to 1/8th" thickness x 10" round.
In a large heavy skillet (medium hot) cook for 15 to 25 seconds, flip and cook the other side ... reserve the pitas until ready to build the gyros sandwiches.
When I'm ready to serve ...
I take a very small amount of the fat that I've drained off from the gyros pan and, in a heavy bottomed skillet (such as a griswold) I reheat the pita bread (whether homemade or store bought) in the fat until warmed through.
... then assemble on the bread the gyros meat, sweet onion, tomato and Tzatziki sauce as mentioned in a post above. (though when I make it, I add some chopped fresh mint leaves as well.)
There you have it.