There are many international shipping and removalist companies and all should be able to provide a estimate of the cost if you know what you want to send and most can provide delivery to your overseas address.
Air freight will be quickest of course but very expensive.
Shipping by sea a cheaper option but very slow..
You need to contact some companies for cost estimates.
Keep in mind when calculating your departure date that your arrival day is counted as day 1 of your first 60 days regardless of the time of day you arrive
You should be able to leave to a neighboring country for a 2 or 3 nights and just re-enter Thailand for another 60 days..
The only thing I would say is don't expect to just keep doing that several times consecutively as at some point in the future the Thailand immigration may question you about being a genuine tourist and could refuse entry if they believe you are trying to live in Thailand on just tourist excemption entries.