Full Disclosure – I have worked in the insurance industry (claims and underwriting) for 15 years in personal, commercial and specialty lines. In terms of saving yourself money, you should understand pricing models can vary dramatically from carrier to carrier. The company offering best price/coverage for senior citizens might be totally non-competitive for someone with young drivers.
Since I was 16 years old, I had my coverage with carrier A. Because they offer good service and I liked having an agent, I have been very satisfied. When I obtained competitive quotes, carrier A's pricing was competitive and I never seriously considered moving coverage.
When I got married, I moved my wife onto my policy. For reasons that continue to baffle me, carrier A charged more to insure her '04 Corolla than my '07 Highlander.
Annoyed by this pricing oddity, I obtained a quote from USAA for matching coverage that will save us $600 per year.