One can never fully prevent an animal from having a large vet bill (trauma, acute illness, etc) but one can do their best to prevent it by keeping their pet safe, not allowing them to roam, keep the house safe, and take them to the vet early on in illness rather than later (like when the gut is starting to die off in large sections due to a string foreign body). (Also, NEVER pull on a string that is caught 'between teeth' or 'under the tongue'. You do not want to know how a gentle pull can severely destroy your cat's (or dog's) intestines while bunching them accordion style.)
As for insurance, I have no opinion either way, having never dealt with it (I'm a one woman show and mobile). When income is tight I suggest putting money aside, as above, selling anything that belongs to you and isn't nailed down, and seeing what luxuries you might manage without (expensive coffees, toys, cable, etc) or even redoing your budget.
Care Credit is useful but it will absolutely bite you in the ass if you don't pay it off.
And at the end of the day, if you don't feel okay about spending thousands for a surgery or procedure, especially one with a poor prognosis, then don't. We all have to make choices.
But basic vet care and evaluations are an important part of pet ownership. That includes annual (or twice annual) exams and early treatment for illness.