You need a router which can act as a media server and ideally you want a usb3 port instead of usb2 if you are going to be doing a lot of reading and writing from the drives. Personally I would take a look at look at
this (lots of other benefits with respect to future proofing) but if you have a look down the range you will see lower models which do the same thing. They do mention that you can get an ac1200+ with a usb3 port. Once you have found a router you might like I suggest you google it and look for a review on smallnetbuilder. They do cracking reviews and tests all aspects of a routers features including storage performance. As an example,
this is one for the EA6900, look at page 2.
Tbh though, if you are looking at remotely accessing files I am not too sure how good a router would be at doing that as the host. I think you would be better off looking at a proper NAS which is designed for that kind of thing and has the features built it. As a very quick example, you could look at something like
this.