I echo mostly what Kean 1 says. It's mostly about playing careful and cautious.
The two biggest problems are:
1) accidental crimes - often through me pushing a wrong button (user error) and drawing my gun, hitting them with a horse, or aiming at someone I meant to talk to etc. It's annoying because the complexity of the controls make this a semi-regular occurrence, but I have just learned to play more slowly, be more careful about what buttons i press in towns, and as I get more used to the controls it'll get better. Dont ride through streets, walk slowly, keep guns holstered etc - what Kean says If I do make a terrible error, I just reload a previous manual save and start over (I strongly suggest regular manual saves because of this issue).
2) high bounties - yeah the bounties (esp after story missions) can be high. But not crazy, nor unplayable. To pay off the story $300 one, for example, I stopped doing missions for a couple of hours, just sold almost everything I had, and hunted for a bit plus robbed a couple of people without getting caught. Took about two hours (starting from about $10 and a bunch of regular items) - and although irritating, I enjoyed the hunting and exploration and found all kinds of stuff while doing it. then went to post office. Bounty cleared, job done. I now try to keep a bounty reserve fund in cash on me - about $100 - as I go, to make paying bounties off quicker and easier.