I reproduce mostly by cloning from existing plants and rarely use seed.

Some of each, it depends on how unique the variety is or how long it takes to start plants from seeds.

Actually the three methods work !
If you want a head start, buy a plant, wash off the soil and plant it in a hydro system. The smaller the plant, the easiest, as the root system is still small. Cloning is another easy option. Starting from seed is kind of "magic" because you see it grow every day, and you enjoy having it done all by yourself. Takes a little more time, and planning ahead.
So if you are a newbie (as we all were, once) start experimenting with plants, you'll see immediate results. I planted Hippeastrum (Amarillys) for fun as a winter project, and it worked perfectly. I used bulbs in a colander, a bucket and an air pump. That is all you need.

what type of propagation would be the best for what you ar doing? i do my hydroponic masclun salad mix from seed, my tomatoes are generally clones, and my herbs are often washed soil plants. hope this helps. ~R

If you use an ebb-and-flow system you can use either method (seeds or plants washed clean of soil), but if you are using any kind of drip system or emitters I'd start with seed, otherwise dirt particles and gook can get into your emitters and might clog them. Roto rootering your drip lines and fittings (if you can't replace them asap) is quite a task.

probably safer to use seed and quicker easier cheap plants at first. Once past the learning curve of your units and gaining confidence move on to rooting cuttings or starting plants. One advantage to hydro is the lack of the soil born organisms so when washing wash well.