Hello Liz, and welcome to the Mammillaria Forum. For the record, you are our 200th member!
Now to try to answer your question. AS always, I am going to say it depends. But on what?
There are thre eor four factors, I believe - compost; pots; watering; and where you keep them.
Basically cacti like to drink water for very short periods, so you don't want to have them in wet soil for any longer than you can.
Most cacti like a very porous soil, with lots of grit, to let the water drain through quickly. I don't know your home country, but in the UK where I am from, we have a compost callled John Innes. I use 30% of the No 2 grade, 30% horticultural grit and 30% of something called Terramol - it is a sort of small particle baked clay which I get from bonsai growers. Some use a type of cat litter which is actually very simlar.
Terracotta pots will dry out more quickly than plastic pots. Some people swear by them, but for others it makes watering more difficult and onerous. Personally I use plastic pots, as they don't let the compost dry out quite so quickly, and so I don't have to water quite as often as when (many years ago now) I used terracotta.
Watering appears to vary - some stand their pots in water until all the compost is wet, and then leave to drain. Others (like me) water each pot from the top, using a watering can to pour the water around the plant until water starts to come out of the bottom of the pot, and then leave to drain. Others just get the hose pipe out and water that way!
It also depends on where you keep your plants and how hot it gets where they are. I have a greenhouse, and use plastic pots, a porous compost and water about every 3 weeks in the growing season, which is between April and end September here in the UK. Then no water for most species until the next March or April, a bit variable depending on the weather, and a 6C temperature.
So no straight answer, as I know many growers who use terracotta and hate using plastic pots.
But if you do use plastic, buy good ones, which don't get too fragile if exposed to the sun for a long time.
Please ask more if this is too indefinite an answer.