Every state government independently regulates the title industry, so practices, prices and rules vary widely. Get to know what goes on where you live to make an informed decision. You said be specific, so here goes:
The CUSTOM in MI is for sellers to pay for the Owner's Title Policy, though custom is not always followed. Buyer pays for the Loan Title Policy for their Lender if there is a loan and also pays for any extra coverages on either policy, called Endorsements. In MI, Buyer customarily pays the closing Escrow Fee and the seller pays the State Transfer Tax (ouch in MI). Regardless of custom, if you pay for the Owner's Title Policy, you choose the title co. and so you should be able to ask questions from your real estate (R.E.) pros (pros being realtor, real estate attorney, loan officer) to get info to make your own decision on which title co. to use. You can call title co's on your own, but in the last few days of any month they are busy and will have less time to talk. I'd ask a R.E. lawyer if you have one.
The title industry is complicated and even most R.E. pros don't truly understand it, though they know more than property owners who have rare real estate experiences.
It is not acceptable for a lender, realtor or attorney to insist the title company is their decision to make. It IS true, however, that these pros may know which agents or direct title company offices give the best service.
The title industry in MI is dominated by Title Agents, meaning locally owned independent companies who issue policies which are underwritten by the assets of large, national title insurers (a few not so large). The agents are held to certain standards regarding underwriting decisions by the national co's, but the service levels they provide can be very good, very bad or anywhere in-between. The large title insurers also operate their own company-staffed offices in many parts of the country and those are Direct operations, not Agents.
The reason I detail this is b/c there are many title agents in MI which are owned by real estate brokerages. When a title agency is owned by a R.E. brokerage it can legally obtain business by telling their realtors to direct their listing clients to their own "captive" title agency. R.E. attorneys and lenders can also be title agents in some states. If a R.E. pro has an economic interest in a title agency that is used in a transaction they are involved in, that interest must be disclosed in writing to the seller and buyer (often this is not done until the closing!). RESPA is Federal law prohibiting kickbacks or referral fees to realtors, lenders, attorneys or anyone who directs real estate business, among other things. It is not a kickback for a title agency owned by a R.E. brokerage or lender to make money by providing title and/or escrow services to listing or borrowing clients, or for a R.E. attorney to generate revenue by functioning as a title agent. R. E. pros can fight over which title co or agent gets a deal without the consumer even knowing!
Sometimes when R.E. pros are also title agents in a deal they act in their own best interests rather than those of their clients, so it pays to know what is customary where your transaction is located. When a seller can negotiate away the responsibility of paying for the owner's title policy to the buyer but the seller's realtor or attorney has a title agency, they might not want to lose the title order and tell their own client they should pay for the title policy -- because if their client isn't the one to pay then they don't make the extra revenue by issuing the title policy.
Can you tell I prefer to use direct offices of title companies? I do not like the unavoidable conflict of interest when R.E. pros are title agents in my deals and I usually don't permit it - I want neutrality but without paying more than I should. I'M THE CUSTOMER, I DECIDE! Yet there are many very good title agents out there. Metropolitan Title and Seaver Title are big independent title agents which operate in MI and do a good job.
In MI, title policy premiums are filed officially with the state insurance authority, cannot be deviated from and the cost does not differ greatly between title co's. If you obtained a title policy from the acquisition of your home, depending on the age of that policy you can get a discount on the new policy, often called a Re-Issue rate. If your title policy is too old, it may not qualify for a discount. If a buyer is paying for title and the seller got a prior policy, the buyer may be able to get a discount using the seller's prior policy. Again, rules vary by state. Be aware that when a title agent is operated by a realtor or real estate attorney, they may discount some of their professional fees (bundle) if they provide title services, and a fee they quoted you for certain services may be under the assumption that they will gain supplementary title revenue.