Printing some thin wall figures from Thingiverse is nice, but not that useful. In my case I bought the printer to be able to print functional things, not decorative. The best material for a starter to use is then ABS. But printing strong functional parts is more than choosing the right material!
One thing that helps objects in all materials from being teared apart is a smooth outer surface that makes it more difficult to initiate new cracks.
This can be done by heating the outer (and when possible inner) walls of the object. Make sure you do not overheat the plastic and make it burn, and make sure you do not put to much heat in the object itself to keep it from warping. Finding the right temperature is not that easy. A standard hot air gun can be used… with a little practice in time and technique this gives great results! Another smoothing technique for ABS is dissolving in acetone. You can apply it to the object with a brush (this did not work well for me) or pour a little acetone in a large glass container, heat it up a bit by placing it on your heatbed and hang the object inside. I’ve never tried that myself since my printer stands on my desk where I also do other stuff and I do not want to get high from the acetone… A little bit different is preparing ABS glue and pour it over, or apply with a pencil on, your printed object. Making ABS glue is very simple: take a small glass container, pour in the acetone and put your wasted ABS from brims, testprints etc in it and wait a couple of days for it to dissolve. As the word mentions, you can also really glue parts together with this glue (works remarkably good!). I discovered that putting a very thin film of glue on some light sanded kapton tape is the best possible way to keep warp sensitive parts sticking to the heath bed glass plate, it can be really hard to get them of sometimes! Since I have enough kapton tape and glass plates it is not an issue when I damage them when taking parts of.
Another logical solution to make parts stronger is using more material, which translates into a bigger infill ratio or solid infill. I found out that combining infill each 2 layers is a good option when using low layer heights and that rectilinear infill creates strong bottom and top surfaces (works like different layers in plywood).
Object orientation is also important. The parts are the strongest in the x-y plane, which is logical the print builds up layers in this plane and then adds others on top. When you need parts that can flex a bit you should definitely take this into account! Sometimes however it is not possible to turn the object around because you have large overhangs in the wrong direction then.
Keeping you print hot and letting it cool down as slowly as possible during the print also helps. Place your printer in a closed box or make sure there is no wind that blows away the hot air around your object.
Last but not least a good design always helps. With modern cad software it is very easy too simulate forces and find out where to add extra supports.