The Ubiquiti access points have their own hand-off process, and don't require a controller for them to function adequately. I think that Aruba Instant On access points function similarly.

There are some advanced features that would require either a hardware or software controller, but for basic use - you don't need either.

(Though you do have to install and run their software controller for the initial setup of the access points. After that, you can close it down, and only need to run it to check for firmware updates, or make changes to the access points.)

I believe the dream routers come with their network suite built in, so you're probably good there. I will point out that, if you're using the "Dream Router" (UDR) -- the cylindrical router -- it does cap out at 700Mb routed speeds. . . so if you're planning on 1Gb speeds from your ISP. . . the UDR won't handle those speeds.