Shipping

The U S Postal Service will probably be cheaper; it nearly always is. However, I cannot speak to the speed of USPS vs. the commercial shippers like UPS and FedEx. For a box of any significant weight it's going to be expensive no matter what method you use, so an extra $20 o $40 may not matter all that much. You can explore USPS mailing options here.

I'm sure UPS and FedEx have their rates available online as well.

Be careful about insurance coverage if you need it, and fill out the customs form accurately.

Use USPS International flat rate boxes.

Here are the restrictions for mailing to Ireland:

https://pe.usps.com/text/imm/il_006.htm#ep5821459

Thanks, folks for your answers.