Some fans these days have an "electronic" control (with timer, display, etc.) rather than the old on/off switch. If power is lost to the fan and then power returns (like a power outage), then fan will usually be off when power returns.
So if your fan has an electronic control and you are wiring to just the white and black, it might not work with the remote for this reason. The remote would remove power the same as with a power outage.
If it has an old fashioned on/off switch, the remote could be wired to this and two speeds at that.
As to the universal remote, some are radio frequency and others are by a light signal. With the light signal you need to be able to point it directly at the device so it can see the light (like a TV remote).
With a radio frequency remote, many of these will not work through walls or ceilings. If this will be in the attic and you want to turn it on/off from downstairs, I don't think a remote would work.
My advice would be to have an electrician install a switch downstairs for you to turn the fan on/off. Then the electrician can look at the fan and determine the correct wire size, etc. Should not be very expensive and you will sleep better at night.