If you want to leave the figs outdoors but with protection, then IMO the best-tasting early, cold-tolerant variety would be Ronde de Bordeaux. Improved Celeste is a very early, cold-tolerant workhorse. And any good "Mt Etna" variety (I like Marseilles Black better than Hardy Chicago) would be tasty and reliable but slightly (~2 weeks) later.
But you said "container growing" so I assume that you will be able to put the containers inside a garage or similar during the winter. If the winter temperatures within this structure would get no lower than ~25 F, you could grow almost any variety with a short / medium season. If you want early and tasty, then I'd still say Ronde de Bordeaux. If you want a little later but maybe even tastier, then you could try Smith or JH Adriatic (which seem a bit too tender for outside in Z5).