The BIGGEST problem with cheap flashes is that they probably won't give you auto exposure.
If you use that Nikon-compatible flash, it may actually fire properly, but it will be in full-manual mode. Assuming the flash has some settings to control the flash power, this is usable, but requires some experience and/or some trial-and-error to get the flash power right.
Honestly, to get auto-exposure, you need one that is specifically compatible with that camera and that may rule out some of the cheaper ones. I wouldn't worry about recycle time for your average casual "family photos" type of shooting.
I also wouldn't worry about a flash diffuser. To do a decent job, it needs to be big and bulky (and probably cumbersome) and that means you will probably not use it.
I recommend simply getting a flash that does have a swivel head and can be aimed to bounce off walls/ceiling.
If you shoot with the flash aimed at a white ceiling and it is set in auto-exposure (TTL) mode, you should ge great results.
Good luck. Flash compatibility is a weakness of these off-brand and smaller camera formats.