Alright, before I begin this answer I need to state that I'm not a professional, just an enthusiast, and I would hate to see someone interested in strength training not try it out.
Additionally, while writing this, I sometimes just thought about how I would work out with no hands. That's not meant to offend but it just helped in brainstorming.
What workouts are unsafe for me
I'm going to assume that anything requiring a solid grip, or, both hands gripping is going to be unsafe. Unfortunately, this knocks out conventional barbell training and dumbbells. Barbell training could also be rather difficult due to the different arm lengths.
This is what I wrote when I first started typing this question and I'm going to leave it here. However, after thinking about this more, the truth is that the same workouts that are unsafe for you are the ones that are unsafe for me: where the weight is not under my/your control.
That's the only rule.
Tips on adapting exercises
My first thoughts were that I would mainly stick to machines.
For the lower body, things like the leg press, extension, and curl machines should all be possible. If you go to a fancier gym there could be hyperextension machines for your back. Delt flye and pec flye are still possible. All ab workouts.
For the upper body, I would turn to bands and cable machines. Upper body weight machines could also be viable given they're set correctly. Single-arm workouts should be easier. Some of the grips might be challenging. I had a thought that an ankle strap worn around your wrist might open up some more workouts for you.
There are also some other accessories that might help you out as well. I am not implying that you need these products but I think it is more useful to point out the options available to you.
How do I go about strength training? (My current best guess is sandbag training)
I think the above helps on what you could do. Any machine can be used to strength train. Sandbag training could definitely be cool. I've seen a guy with one arm do atlas stones, so don't count yourself out. Your question is really broad but I think if you asked "How can I adapt XYZ workout so that I can do it with my situation" you'd get some people with some ideas.
General advice for my situation that you think is useful
Don't get discouraged. Being strong is bad-ass and you have every right to want to be strong.
Start slow. Ask questions. Any personal trainer worth their weight should be able to help you out, however, don't be surprised if someone says they don't know.
When you go to the gym focus on yourself. Don't focus on what others are doing. The gym is for everyone and you have as much of a right to the equipment as anyone else paying for it.
Try to go to the gym with family or friends. It helps to have a buddy for motivation as well as for figuring stuff out.
Remember that diet is the larger half of getting strong and looking strong.
Sites/forums and other resources that might be useful for me
I'll edit here if I come across any other ideas.