My family took a leap of faith when we moved down here last year. My wife and I quit our jobs and sold our house then moved. We had debated moving from NY to NC for awhile and decided to make the move while we could still get a good return on our home. Luckily, we were able to sell our home within a month and find a job within a week of being in the Charlotte area.
That said I have met more than a few couples who have bought homes quickly and ended up regretting the decision. My advice is to rent first and get a feel for the area prior to buying. A home is a significant investment and as with all investment one should really understand what they are buying into. Schools, crime rate, population density, all of this and more a factors to consider. BTW City-data is a great repository for this info
Moreover, you want to be able to travel in the towns and get a feel for the people and attitudes that best fit your style.
As for storage, there are many places you can use. Some apartment complexes have garage spaces that you can rent in addition to the apartment. One suggestion here is to Google the apartment name and get reviews and feedback. I can't think of the sites but there are a few out there that do contain reviews that are worthwhile.
We have didn't have pets but there seems to be a pet friendly attitude in many places we've visited. Therefore, I doubt you will have a hard time finding an apartment that will suit your needs. Be mindful though that you may be charged extra.
I wish you luck in your transition and I'm sure that you and your sister should be able to find jobs in the area. Perhaps expanding your scope outside of your sphere may increase the likelihood of you finding work.