It is not atypical in Australia to have no clothes dryer in your house. Our place doesn't even have room for one! We have a lovely four-line clothesline setup on one side of our tiny back yard.
At first it was overwhelming, and I think the fact that it was winter contributed to that, because I had to really watch the weather forecast and dodge the rainstorms. That plus my inexperience really made things difficult and stressful. But now I have a system and I am able to do up to eight loads of laundry in one day.
The most important thing to consider is your real estate and time constraints. A washer full of jeans will require more drying time, but less hanging space than a washer full of socks. Also, some clothes (particularly bright colors) need to be hung in the shade so they don't fade, while other clothes (e.g., your underwear) benefit from exposure to sunlight (the natural disinfectant).
I've worked out a system now: every week I have to do a load of delicates (the clothes I wear to work), and several loads of regular clothes. I generally do the delicates first, and hang them on one end of the clothesline that is in the shade. Then I do a load of socks and underwear, and hang them in the sunniest part of the clothesline. The clothesline is full and I've used most of the clothespins by this point. Then I wash a load of shirts, and when they are done I take down the delicates and the driest of the socks and underwear, and replace the delicates with the shirts I don't want to fade, and the socks and underwear with lighter colors and/or old shirts. Then, I will do either some towels or some jeans and hang them in the sunny part (taking the jeans down quickly once they are dry so as to minimize fading). If I had not done laundry in a long time and I needed to do two loads worth of socks and underwear, I would do the following: delicates, then socks/underwear, then Jeff's button-down shirts (which hang on hangers on the line, so take up little real estate), then the second batch of socks/underwear, then other clothes as above.
Sheets are like socks and underwear in that they require a lot of real estate but a short drying time. I hang them across two parallel clotheslines, which helps them dry more quickly, but takes up quite a bit of space. So if I had to do some sheets I would probably wash them first, followed by the delicates, followed by the socks and underwear.
I also have a portable indoor/outdoor clothes drying rack, which was helpful in the rainier months, but which I now use for overflow. But in the hot, dry summer air here, I rarely need any kind of overflow, especially now that I have my system down.
Now I really enjoy the challenge of hanging the clothes on the line, and it's gotten a lot easier with experience. As an added bonus, I'm saving a lot of money on my power bill, my clothes will last a lot longer, and they smell so much fresher when they are air-dried.