The cheapest type of car to insure is typically an early-2000s 4-door sedan. You want it to be a car that you are not making payments on that way you do not have to carry comprehensive and collision coverage.
When you file a claim for an injury, the party responsible for the injury would be the company to pay for the claim. If you had another injury from the second accident you will be able to file a claim.
Although you have separate car insurance policies, your mutual assets would still be at risk because you are married. Your husband's car insurance would be the one to pay for the damages but if the damages exceed his policy limits for liability then your husband would be responsible for the remaining damages.
Unfortunately, fault can only be determined by the claims adjuster assigned to the accident. However, for the other part of your question, because you were driving your company's vehicle on company time, if you were to be found at fault then the company's insurance would take cover the damages.