First of all home insurance is not the same as title insurance. Sometimes you will see home insurance called fire insurance, even though it covers much more than just fire damage. Title insurance comes in two types, both deal with mistakes in the title. One covers the lender and you must purchase. The other covers you if there is a problem with the title, and you should look into it.
So I am assuming that you want to discuss fire insurance.
In the Unites States many, but not all, insurance companies offer home, auto, and life insurance. If you have auto or life insurance, then taking a look at their home insurance policy makes sense. If you have multiple types of insurance with one company they will usually offer a multi-line discount, some call it a bundle. If you are happy with your insurance policy you already have, it is generally a good place to start.
Besides customer service, the big issue with any insurance policy is do they have the resources to pay what the policy cover if there is damage. In the United States all insurance regulation is done at the state level. You can do research at the state insurance commission website to see if there are complaints against the insurance company.
In some parts of the country there can be changes to who will write home insurance policies. This can happen if there are a series of natural disasters: forest fires, tornadoes, hurricanes. These events can destroy many homes, and over time some companies will want to get out of the business in that state.
If you have a mortgage they will require you to get home insurance. You will have to have made arrangements for a policy before you go to settlement. You may have to show proof of coverage and payment as part of the settlement process. Your real estate agent or the settlement company should be able to provide additional information about the proof required. The mortgage company may have specific requirements regarding amount or coverage, and if things like flood or earthquake insurance is required.
If there is no lender home insurance isn't required, but you will still want it to protect your investment.
For me if the insurance company is solid, then price is the biggest concern. Make sure that when you get quotes it is for the exact insurance coverage you are going to purchase. If you can't do an apples-to-apples comparison then comparing quotes is impossible. So talk with the lender or the state if there is no lender about what is required.
Also if you don't have life insurance already then look into it. You mention we in the question and adding a home to the mix makes it more likely that you will need life insurance. If you already have life insurance then this is a good time to review how much you need and have.