It would be good to understand what your experience level is, but I assume you are a fairly new certified diver that has been renting gear until now. Also, it looks like you are looking to purchase on the internet. If my assumptions are wrong, I apologize.
Some smart dive shops will match online pricing. But what you get in experience and knowledge is worth paying 10 to 20% more! Sometimes they will includes some air fills or maybe a free tank rental, something you can’t get online. A good local dive shop will make sure you are getting sized correctly, ensure hoses are the proper length and in general a wealth of information, especially for someone buying their first set of gear. You would be much better serviced and if you have issues, you have a place to bring your gear back to for resolution. And, I would think if they need to send your gear out for repair, they can lend you stuff!
With that said, you only know what you know, so tough to make a decision on a jacket vs back inflate BC now. Of all your gear, the BC is the one piece of gear that effects how you feel in the water, your comfort and freedom while diving. With respect to training, there is no difference between a jacket and back inflate BC. This is coming from someone that has been diving a Tusa, jacket BC, for many years and just switched to an Aqua Lung Rogue back inflate BC. My Tusa BC, still works great, but not getting squeezed when inflating is liberating, my arms and shoulders have no restrictions, and even more important, the back inflate BC keeps me in a very comfortable horizontal position under the water, rather than the angled head up position with the jacket. I wish I made this change years ago! Your dive shop should have demo or rental gear to let you try a back inflate BC. Usually, if they charge to rent the BC, they should put the cost of rental towards your purchase, so it should not cost you any more money. I know you are chomping at the bit to buy your own gear, but be patient and try to make good Informed decisions.
Good luck and safe diving!
Jeff
P.S. I do not work for a dive shop, but if you are in Southeast Florida, I can certainly recommend a great one.