It is good that you think about the dangers.
You will get over your fears as soon as you understand the dangers involved.
Portable powertools differ.
Something like an power-sander or a dremel should be safe (I let my 4year old one work on a scrap-piece of plywood with a dremel, he had safety googles, earmuffs, gloves and a great time).
Jigsaws should be quite safe, as long as one can think about where he places his fingers while he saws away (the professionals use a barrel-grip saw and place them under the piece, so that the blade points upwards. That way the material on the upper, visible side won't splinter, as the blade cuts downwards into the material, while they can observe and direct the cut). Kickback can happen, but are light. I'd place a router in the same area.
Circular saws are to be respected for their kickback. Riving knifes will reduce kickback significantly. Circular saws without them are illegal in my jurisdiction.
Chainsaws (yes, those are not really tools for the fine woodworking) produce a lot of injuries per year. Don't operate one without proper training.
Bandsaws, jointers, tablesaws and perhaps lathes are one of the most dangerous things out there in the trade. It isn't wrong to have an healthy respect for them. Those should be only bought and operated after thorough training. Courses are a good way to be familiar with them, as you can operate them under professional supervision. Just watching some Youtube videos might not cut it..
The most important thing is about how you work: Have the piece firmly attached, have a good light and be calm and attentive. Much more accidents happen when one is in a hurry, while being exhausted, in the low-light, holding the workpiece with one hand while sawing with the other hand.