Are you moving to the DR for good? If so then you enter on a visitors visa and apply for residency when you are there.
Temporary residency costs around $800-$900 if you go through a lawyer, takes around 6 months to come through and is valid for a year from the date of issue. After that year you can then apply for permanent residency which I believe costs about the same again.
The lawyer will handle all the paperwork for you and you will be required to travel to Santo Domingo to have a urine, blood test and x-ray.
I am not sure what the ?170 on the Dominican Embassy website was for - it's too cheap to be for residency so it's probably for an extended visitors visa, however you don't need that. If you are only planning on staying in the DR for a few months or a year then the fine you will be required to pay at the airport for overstaying on your visitors visa is peanuts compared to paying ?170 for an extended visitors visa. There is a thread stating the overstay fines - just do a search to find it.
Note that if you are planning on driving whilst in the DR then your UK drivers license is only valid for 90 days (which resets each time to re-enter the country). If you are driving whilst your residency application is in process (>90 days) then get a copy of the paperwork from your lawyer as proof of application and keep it with your driver's licence. This will enable you to drive with your UK licence up until you receive your residency, at which point you can apply for a Dominican drivers licence.
Daydream