The dangers of self-injury are generally small (depending on the injury of course) but worth considering. A few simple principles can make you much safer.
For more detailed discussion, see Cutting The Risk.
As anyone who works with knives will tell you, sharper blades are safer. A blunt blade is more likely to slip. Really sharp edges like razors blunt very quickly and are difficult to sharpen again, but that's probably a good thing since reusing the same blade is risky for the same reasons that needles shouldn't be reused or shared. Surgical scalpel blades are probably the ideal disposable blade and can be ordered cheaply online. Glass can be very sharp but is not recommended because the edge may flake and leave tiny shards in the cut. If you decide to reuse a blade anyway, make sure it's kept clean and sharp between uses.
Infected injuries are relatively unusual, but burns and deep cuts are higher risk than everyday scratches. Any blades should be clean. Any break in the skin should be cleaned afterwards, ideally with some kind of antiseptic wipe or lotion, and covered with a plaster or bandage if possible. All basic first-aid principles apply. Scalpel blades can be ordered sterile.
If you want to reduce scarring, the injury should be allowed to heal quickly. This means making sure it's clean, but otherwise avoiding disturbing or interfering with it. Shallower injuries are less likely to scar.
If you're bleeding a lot more than you expected, and especially if it comes in regular spurts, then you've likely hit an artery and need urgent medical help. Arteries are generally well protected, but they come close to the surface in the neck, inside arm and inside thigh - it's best to keep blades away from those areas.
If you're looking for pain and not picky about the source, it might be worth trying out things like touching stinging nettles, plucking hairs or holding ice on sensitive skin rather than slightly more risky options like blades and flames.