I love asters and have them is several locations. They will do just fine in average garden soil. Just be sure they have good drainage. They don't want a lot of fertilizers or amendments. The soil can be a little lean & sandy. The biggest factor is water. They can't sit in water or mucky saturated soil. Let them dry out between waterings.

Do you mean the annuals or the perennials? The perennials are very tolerant and don't seem to mind. I've known them do well even in really poor heavy clay without any care of feeding (poor things!) though the advice is they like fairly good drainage..
I've not grown the annuals.

For heavy clay, I'd work in a small layer of compost -flowers will last longer. Both types need good drainage & lots of sun.

Hi, before we can give correct information, we need to have some idea which of the 250 species of Aster you're asking about, Asters are divided into 3 distinct groups, depending on their cultivation needs, group 1 need well cultivated, fertile, moist soil in full sun or partial shade, group 2 need well drained , open, moderately fertile soil in full sun, and group 3 need a moist, moderately fertile soil in partial shade.
Asters can be annuals, biennials, perennials , and sub shrubs, ranging from well drained mountainous sites, to moist woodland, so we really need to have some idea of the species, or even a varietal name may help, Derek.

Alpine species and hybrids will need more drainage than standard Michaelmas daisies, as will the Mediterranean species, such as Aster amellus. All Asters are subject to mildew if they don't get enough direct sun.

They all seem to like average to lean garden soil too.

I haven`t bought them yet,looked at some on the garden centre they were in pots naturally but by their size would say perennials from last season.

Good sized, then, with clustered stems from ground level? Ordinary all purpose mix for pots, or any good garden soil for out in the ground. Amend heavy clay soil with sand and organic matter for best growth, though they can stand a fair amount of abuse.
Derek, I haven't run into group three Asters yet, but that may just be because they are likely harder to grow in the desert.

Hi Tug, yes I think desert conditions would be quite demanding for group 3 Asters, you would be forever watering them, Derek.

Lol! We're forever watering everything, here! But group 3's sound like forest plants, and, unless they are from a tropical forest, they aren't likely to take the hot nights of the monsoon season, even with extra water. With many temperate zone plants, the high air temperatures often cause certain of their vital enzymes to just shut down.

I was surprised to see palm trees planted among the cacti when I visited Scottsdale, AZ. They seemed out of place to me.

Some landscapers call that the "distinctive southern Arizona style", while others call it the "give the tourists and the snowbirds what they want" style. :)
It's difficult to keep it from looking random and disjointed, but some designers pull it off amazingly well. Others...not so much.

They did look disjointed. I don't suppose they last very long.

Hi Tug, I think most of the group 3 plants are native to E North America, so not from tropical forest, so you're probably right, Derek.

Bathgate, Phoenix, Brahea, and Washingtonia species are quite drought tolerant, and compatible with cacti, as far as watering is concerned. So, for good or ill, such landscapes can last for decades, if cared for intelligently. The most successful ones are based on a Spanish Colonial style.