I have been through the residency process so I speak with some authority, unlike some who never bothered to become legal. First I would advise you to be sure you want to live here permanently and for more than three months at a time. Visit and make sure. Then, if you have at least $1,500 US in pension and/or social security income, getting a retiree residency is fairly simple and straightforward and should not take a very long time (six months at the most). Meanwhile, while your application is pending, you should plan to stay in the country. You begin the residency process by getting a residency VISA in your home country at the Dominican embassy nearest you. The best source of information on what you will need is the immigration website for the Dominican Republic
https://www.migracion.gob.do/ The pages can be translated into English. Then you need either a person very familiar with the process who speaks spanish or a good attorney who specializes in residencies. Your total cost from start to finish will likely be about $2000 US. Your initial residency is good for one year (I think) and then you can renew for up to four years. Your passport must have a least 18 months before expiration. The retiree residency allows you to skip over the five years of temporary residency for other people. Or if you are wealthy and plan to invest in a large property, you could qualify for an investors residency, similar to retiree but with different requirements. When I first moved here, I did not have any income at all but had money in a Dominican bank account that I had wired here on the sale of my house. For a normal residency (not retiree and not investment), the criteria is that you be financially solvent and you would probably also need a "guarantee" from someone (usually your attorney or someone designate by him or her). They also require repatriation insurance (to pay for your airfare home should you be deported!) that is about $100 a year. It's easily obtainable. The only tricky documents are your birth certificate that must be recently obtained and apostiled (special stamp and approval from your state office) and a certificate of good conduct. That used to be obtained from your local police force (in my case Prince William County Virginia), but I understand that now it must come from the FBI and you need fingerprints from the US as well. That's more complicated, but everyone has to do it so it happens OK. My neighbor just did a retiree residency last year. You must have residency to obtain a Dominican driver's license, which you need if you want to drive and be insured legally.
So far as health insurance, you can obtain it very easily if you apply before turning 65, which I was able to do since i moved here at age 60. I have a group plan through a friend's apartment rental company where I lived my first year here and I pay only 1100 pesos (less than $30 US) a month. I have only Part A Medicare in the US. I do not return there for medical care. I am very comfortable with the doctors and care I receive here despite speaking little Spanish and having two incurable life-threatening illnesses. My insurance pays 100% of hospital and emergency (except for a private room supplement) and 80% of everything else up to the limits. I've had just about every test imaginable and the most I've ever had to pay was about $100 US. I did pay $300 out of my pocket for my bone marrow biopsy to be sent to the US for interpretation and examination. My doctor copays are 500 to 1500 pesos ($10 to $30 US). I do not have prescription coverage but it is available with most plans. Most medications are available without a prescription and I spend about $300 a month.
Yes, your social security can be deposited directly into your Dominican account. There is a form you must return once a year to say you are still alive and living overseas. Opening a bank account can be trying, like many things here, but it is doable! I do not have my social security deposited here directly now but might in the future. Like you, I did not want to pay Virginia taxes on my 401K withdrawals so I do not have a residence in the US at all.
If you have other questions or concerns, just ask. I'm single (alone and happy) so don't let anyone discourage you from retiring here is you want.