Best way to make your own mine in survival in minecraft?

Make it 6 by 4 with lots of different passages and make it like a storage place too with a lot of torches and signs to label the passages

Make a quarry. Strip mine in a square, with a large open center and either a staircase, mine cart tracks, or both going down into the lower levels. Light up as you dig deeper. This not only prevents mobs from spawning, but if they accidentally fall into the quarry, they'd most likely die from the fall damage.

Later on, you could opt for an elevator (redstone or just a plain water elevator) to make getting in/out easier. You should also invest in some minecarts with chests built in them to send off your gathered materials. This gives you a lot of cobblestone (a really great building material resistant to Creepers) along with other materials such as Iron, Diamond, Gold, Redstone, and others (if you're lucky to find them).

You can also make a rest stop along the way, with an anvil, furnace, crafting table, etc to restock on food, tools, or to convert ores into bars.