Flank steak is one of the more lean cuts of beef. I am not sure if it is leaner than eye of round, but the leanness causes it to be very dry without marinating it.
Flank steak can be pretty expensive. A similar cut is called skirt steak is cheaper and marinates well. A difference with skirt steak is higher fat, but it is not near the highest fat content. One steak can serve three to four reasonable adults, so it is economical despite the price per pound. They are usually packaged with at least two steaks, rolled up for some reason. You can freeze one or double the recipe if there is a meatasaurus eating.
Many good marinades can be used that take inspiration from around the world. There are even some decent commercial marinades, but it is always better and cheaper in the long run to make your own.
This recipe is at least vaguely southwestern US cuisine; somewhat similar to what you might expect to see in Arizona. A few tweaks could make it seem more Tex-Mex or Mexican than Southwestern.
Southwestern Marinated Flank Steak
1 1/2 pound-ish flank steak 1/2 cup of lime juice 4 cloves crushed garlic 2 tbsp dry oregano or about 1/3 cup of fresh oregano leaves 2 tbsp olive oil 1 tsp pepper 1 lime sliced Put the steak in a container that can be sealed, mix all of the ingredients in a bowl, and pour into the container and seal it. Marinate at least 6 hours, 24 is better, shaking the container every so often. Set the oven rack so the steak will be 2-3 inches from the top heating element. Set the oven to broil. Place the steak in a pan, preferably with a broiling rack in it. Cook for 5 to 6 minutes, until it is brown. Turn it over and cook for the same amount of time. Let it sit about 5 minutes to cool. Slice it thinly across the grain.
Since this steak is lean, cooking it to medium or above will result in a pretty dry steak, marinating notwithstanding. Cooking it until the center is between 135 and 145 turns out the best in my opinion.
Spicy rice (or quinoa) dish would go well this, I will try to come up with a good companion side dish. As always a good salad, with a red pepper dressing or something made out of habanero would be good as well. If you are into dessert a lemon meringue pie, lime sherbet or even a Key Lime pie goes great. There are lemon based Mexican and southwestern desserts that I can not think of at the moment, but anything cold, sour, and light tasting goes well with this.
If you like it, the steak goes well with Guacamole on top.