Don't know about pricing on shipping containers....
I rented a 26' Penske cargo box last week and Corpus-->Friendswood-->Beeville-->Corpus was just over $400 after fuel (1 day rental). But I just checked on their website and they do rent flatbeds as well; but they might all be CDL (class B) required. The container alone should be light enough that you can put it on a <26,000# GVWR truck, but finding one to rent could be a problem. If you can rent the right truck, or find someone with a Class B or greater license, then your biggest hassle would probably be unloading.
Your other option would be 3/4 or 1 ton truck with a flatbed gooseneck trailer and haul it yourself that way.
Either way I don't think transportation/delivery will be your expensive part. Unloading it unless you can get your hands on a forklift will be the problem.