Since you want to grow it in a container you will have the luxury of being able to move it around if necessary...
Container size depends on the size of the plant...
True, this is not really the best time of the season to transplant a clem in TX I'm sure, but if the gardener wants to get rid of it right now it's worth a try.
How big/old is it? who will dig it out?
That is probably the most crucial step in preserving as much of the root mass as possible...
OP says a 'start'--to me that implies a small or young plant, but the subsequent post gives the impression of something larger and more established.
Maybe dig it in the evening and keep it moist but not soggy and as cool and shaded as possible initially...like the north side of the house? and then move it to the east side after it recovers a bit?
What kind is it?