I was recently asked by a beginner what are some tips to keeping safe around her 2 year old gelding that spooks a lot? Here's a few ideas. Please add to my list, if you have any safety tips for working with horses!
As far as staying safe, the more you watch horses and are around them, the better you will get at knowing the signs to watch for when they are about to move. Horses run or shy from trouble, and the slightest thing can make them run clear across a pasture. So learn to watch your horse's ears, head position, tail, and placement of his feet.
For instance, your horse is sleepy if he has one hoof cocked (bent and resting so his weight isn't on it) and his head and neck held level or drooping. Your horse is startled and ready to bolt if his head and neck are held high and stiff, with his ears back, and this also may indicate that he may kick. Your horse is interested/inquisitive/curious if his ears are pricked forward and he seems to be staring at or watching something. Knowing general behaviours in your horses will help you stay out of harms way if they spook or run. So watch them and spend time with them.
Some things you can do with your gelding is work with him on a lead line, and get him used to new things. He may develop a strong attachment to the mare he is pastured with. A lot of geldings become "girl crazy" if they are kept with mares, and when you take him out alone, he might whinny for her and try to always go back to the barn. So if you can get him to focus his attention on you and take him out on walks (as long as he is gentle to lead and won't pull away from you--you may need your dad's help at first) to get him used to being with you, rather than with his pasture mate.
If he is overly attached to her, you can ask your dad to help you tie him safely out of sight of her for an hour or so. If he stands quietly you can brush him and pet him and just be around him. If he whinnies, paws, tries to get loose, or fights the rope, get far away from him and just watch. Don't try to go help him if he gets tangled in the rope (many people are severly injured when helping a panicking horse--I speak from experience and have the scars to prove it). The best thing to do is wait until he is completely calm, and then go to him and untie him. Tying him away from the mare will give him more confidence in being alone, so that when you ride him, he will listen to you better and not try to always return to the mare.
I think as far as the bucking thing, there could be several causes. Most newly started colts will buck once or twice, just as a test. Some horses buck if the saddle hurts them, or doesn't fit right. Some horses buck because their owners feed them too much high-energy grain, which makes them feel ornery and feel like goofing off. Some horses buck because it is their natural reaction to any situation they don't like...and that type of horse will persist in bucking the rest of his life, whenever something comes up that he doesn't understand or accept.
I have a mare that started bucking when I rode her because I wouldn't let her return to her pasturemates. She has been worked with by a professional trainer, and still bucks when something comes along that she doesn't like. Some things that will help me with her are 1. tying her away from the others at times to get her used to being alone/with me. 2. I switched from a plain ring snaffle bit with no curb strap or shanks to a training bit with shanks and curb strap, with a broken (hinged) mouthpiece so it's still somewhat like a snaffle. (I always start out young horses in a plain ring snaffle.) 3. ride her more often, longeing her at a trot for awhile before I get on her, so she doesn't have extra energy that makes her want to buck, and 4. pay attention to her ears and body language so I can pull hard and prevent her from getting her head down to buck. These things have all helped me ride her successfully, even though she is more prone to buck than other horses I have trained.
I think your gelding will make a fine horse as long as he continues his training, and doesn't develop any bad habits. Some other rules of thumb are: don't feed him treats by hand...always place them in his feed pan or even on the ground. Horses sometimes start nipping at their owners wanting more treats. So if he acts pushy or nips at you, don't give him treats for a long time. When leading him, use the lead line to keep him out of your personal space. He should not lead you--he should walk beside you, even with your shoulder. If he gets too close or steps on you, you need to use the end of the lead line, swing it in a circle at him to get him to move away. If he doesn't move away, swing it hard and hit him behind the shoulder with the end of the rope. (Never hit him in the head or face, as it could make him head shy...they only instance where I would hit a horse's face is if he bit me, and only if I could slap him immediately. They only understand it if it is quickly after what they did wrong, just like another horse would do.) If your gelding bit your mare, she would instantly lunge at him, bite him, or wheel and kick him hard with both heels. Horses understand that, that's how they treat each other. So don't be afraid to hit him if he does something mean to you. Just stay safe (away from his heels) and hit his shoulder or side where it won't scare him or hurt him.