PAR "20" is the diameter of the bulb. The unit is eights of an inch, so 20/8= 2.5".
Focal spread of a bulb is a parameter of the bulb. They vary from 8 degrees (spotlights) to 120+. Naked bulbs are a 360 degree sphere in all cases except LED, those are a 160 degree cone. It only takes a little lensing to make LEDs kick any angle you want.
Whereas with halogens, they require a reflector to focus. You get two lights, the unfocused direct light from the filament, and the focused light bouncing off the reflector.
You shouldn't have any trouble getting LED PAR20s of an angle of your choice. It can't spread any wider than the enclosure allows, that is to say, blasting light on the inner ring of the enclosure is not useful.
If your base is E26 (26mm diameter), that is the classic Edison base that is universal in North America. That, or E10 candelabra, are the only two bases I would consider using. Any other base, the lamps will be expensive and of limited selection. However, that said, going with another base will allow you to use an adapter which will take space, allowing the bulb to hang lower, clear the enclosure and let you use a wider arc. They make E26 to E26 adapters, they typically have pull switches on them.