Shipping small bits of furniture from US cheaply

My mom has her original play table and chairs from when she was a child in the early 1940s in Texas.  She doesn't have space for them, but we'd love for our daughter to have them.  She also has a cherry wood, handcrafted high chair from 1940. 

These pieces can't really be broken down, so we're wondering on the least expensive way to get them across - UPS, post office, or some other commercial firm?  Time is not an issue.

ANY advice appreciated!

Since you just have a little bit of stuff to ship, I'd say the USPS (if it's all reasonably small stuff).  If you're not worried about time, just send it surface mail and ideally it'll be over here in about 6-8 weeks.  Pack it really well and insure it.  And I'd wait until after Christmas to send it....I'm always worried about sending things this time of year!