Okay so lets get started:
The best way and least expensive way to ship your belongings to the country is AFTER you have filed for residency! With that you can bring one container of personal items and one vehicle.
There are a number of specific rules. For example you cannot ship 8 brand new tv's as you will end up paying tax and duty on them. If you are going to ship bring things you actually own and use! Upgrading to all new electronics a month before is not a great idea. Buying one additional tv is probably okay.
NOTE: almost everything is readily available here now. Some things are more expensive UNTIL you calculate shipping etc. So plan wisely.
Another consideration: what you used at home may not be practical here! For example due to the price of electricity almost everyone cooks with propane! You likely dont want to ship your electric stove.....
Costs: shipping, some taxes and duties but its much much lower, you will need a customs clearing agent who knows what they are doing. Do not use your friends cousin! Get a professional, you will be much happier.
I will cover process in general below.
WITHOUT RESIDENCY
If you are wanting to ship a large amount of personal items, furniture etc to the country without the residency exemption be prepared to pay the price!
Customs can and will allocate values at will and on a whim to your items. Your 5 year old TV could be treated as if you bought it here new.
COSTS
Sales Tax is 18% on the assessed values! Duty is anywhere from 10 to 40% on the assessed values. And no there is really no way to "appeal" the assessed value. You can, however, propina it down a little!
Shipping is the same costs. And in this case even MORE important to have a professional who can clear your items.
PROCESS
Before it leaves make sure you have a complete and accurate list of what is in your load. TAKE PHOTOS! Have as much proof as you can. If you have receipts for purchases keep them accessible. Make sure the manifest is correct.
Send all of that to your customs clearance person in advance of the shipment arriving.
Once it arrives - you and your agent will be notified. It is critical you get the process done as fast as possible. They will store your items for 10 days! After that you will be a daily storage fee regardless of who is at fault for delays!
Understand the people who run this are not interested in your timeline nor your problems. They just want to get through their day doing as little as possible. The right agent help push things along.
Once you pay for your clearance and fees - there are a bunch of little fees, storage if applicable, taxes etc... then you need to get your items out.
Your agent will be there to go through your shipment and confirm everything is there. Then you move it out.
IF it is an entire trailer then it must be moved by a union truck. If it is smaller then you can take it out.
The entire process does not need to take forever but it can! It can take months if something is not right or is in question especially with vehicles without residencia.
FOR SMALL SHIPMENTS
For smaller shipments there are a few specialty companies who do blue barrels and or boxes. They handle the process start to finish.
You can also use a freight forwarding company for things like a BBQ or appliances you buy in the USA and ship by boat. Normally they handle everything start to finish including delivery to your house. They will quote you a full price.
For smaller items or multiple purchases use a mail forwarder. There are many. Use the known names as smaller and newer companies often have issues. Bigger companies include BM Cargo, CPS, EPS, Vimenpac etc.
How it works: you receive an address in Miami. That is where you have things sent from Ebay, online shopping, Amazon etc. From Miami to whatever city in DR is 3 to 4 days. You pay in some combination of weight and size! Check in advance so you understand the costs. AND it must be under US 200 including deliver to Miami! Otherwise you pay 18% sales tax and DUTY!!!! Do not assume that anything in that package will be priced separately. I have seen that happen, 3 purchases of under US 200 each shipped together and they paid all the taxes!
Your package MUST have an invoice except for documents. If you mom sends you a Christmas package she must document the contents and value.
AND now you must upload into the system your copy of the invoice! Without that it is held at customs clearing!