If your budgies will be living in the aviary full-time, bigger is better. It gives your birds more room to fly and it gives you more room to be in the aviary with your birds. Rather than thinking in terms of minimum requirements, approach from the other direction. How big can you make your aviary? There are always going to be practical limits that restrict the size of a backyard aviary, due to space or cost. Only you can decide how big you are able to make your aviary or if an aviary is right for you and your birds.
Regarding risk for birds in aviaries, there are several important risks to consider. First, if you are building an outdoor aviary, like mine, weather is a significant concern. I live in a temperate climate, so it gets hot in the summer time and cold in the winter. When planning my aviary, I had to consider carefully how I would handle normal seasonal fluctuations and extreme temperatures, like during a heat wave or snow storm. If you live in a tropical climate, you might not need to worry about as much temperature changes, but you will still need to provide adequate shelter and protect the birds against bad weather. Ideally, you want to have access to electricity for your aviary, so you can run lights and provide safe heating/cooling options.
Another risk for aviary birds is predation. There are a lot of creatures that would love to eat a parakeet. Dogs and cats, certainly, but also snakes, rats, hawks, and much more. When building an aviary, you want it to be sturdy enough to keep the birds inside but also strong enough to keep predators OUT. The measures you need to take to keep your birds safe will vary depending on what kind of predators live in your area and where your aviary is located. A solid concrete foundation and a solid roof can provide aviary inhabitants with a lot of security.
Lastly, when designing an aviary, be sure to include a safety porch. Always have at least one closed door between your birds and the outside world. A safety porch is a little "air-lock" for your aviary, so you can step inside, close the outer door, then pass through a second door to reach the aviary. If a bird flies into the safety porch, you can just gently shoo it back into the aviary. But if you didn't have the porch, a bird could fly straight out and be gone in an instant. The birds in my aviary rarely fly at the door. They seem to sense that it is a "no fly zone". But over the years, there have been a few times when having a safety porch and following proper procedures when entering or leaving the aviary saved a bird's life. You definitely want to include this feature in your aviary design. It is super important.