I have become aware of ‘neck radius.’ I understand what it is, but don’t understand how it makes a difference. Is one neck radius easier, or less painful, to play than another?
It’s fret board radius not neck radius. The biggest advantage/disadvantage is the smaller the fret board radius the easier it is to play barre chords the larger the radius the easier it is to bend strings. Gibson has a happy middle with a 12 inch radius
Fender have different standards though…
Today, most Fender electric instruments use one of two main fingerboard radius measurements. Most prevalent is the modern 9.5” radius (241mm), which was adopted in the 1980s and is now found on about two thirds of Fender electric instruments. The next most common fingerboard radius, 7.25” (184mm), is a vintage-era spec now used on just under a third of Fender electric instruments.
12" radius is much less used.
Are you talking about fret radius or actually the neck radius?
Honestly, I don’t know one from the other. When ‘radius’ is listed as one of the specs, is that neck or fretboard radius? The reason I was curious is that perhaps I should pay attention to that as a possible way to reduce knuckle pain.
Its usually the fretboard.
The neck is potentially a range of shapes and different radius’s anyhow (tho some fretboards are variable radius too…)
So with fretboards a lower number means more curved , low numbers are like 7.5-8.5 inches , so very curved.
‘Flat’ ish would be 16-17
In general curved is comfier to play chords on but makes it harder to do bends/play lead, so you get compound radius frets that start at 10" at the nut end and end at 16"
All other things being equal, a smaller neck radius can make it easier to play barre chords, but it is just one variable effecting the overall playability of a guitar.
String gauge, scale length, and most of all a good set up, can all have a bigger influence on how easy (and less painful) a guitar is to play.
It is pretty easy to look this stuff up.
Most acoustics run 12”-16”, occasionally 20”, many electrics run 7.25”-12”.
My older Larrivee has a 16-20” compound radius. My Pono 15” and my classical flat, like most classical.
My understanding is that flater is faster and more articulate, easier to bend, whereas a tighter curve is better for rhythm and cords.
You should definitely go and play some different radius fretboards before you let it influence your buying decisions (and I think the same goes for neck thickness/shape).
It’s a very personal experience and there are a lot of online opinions (who’d have thought it!)
I own a 7.25, a 10 and a 12 and go between them without really registering the difference much at all. Others might find their hands, technique or playing style exaggerates the differences.
Paul.
I think a guitar is made up of so many details , fret radius,width, fret heights, neck shape, scale etc etc its hard for someone new to get dialed in to what works for them and that is likely to change quickly anyhow
Well for me it’s not like that 
My first guitar is a Fender Strat, small neck. Then I’ve bought (for me my dream guitar) a Gibson Les Paul Goldtop, the Slash Victoria. Compared with my Fender, the neck feels huge (it’s a C shape, little smaller than a 50’s neck, but larger than the '60 models). I have “smaller” hands, so in the beginning, it was a huge difference to play. But the barre, they’re like 50 times easier to play. I still make some mistakes sometimes, but when i play my strat it’s the opposite 
i sometimes don’t make mistakes when playing a barre.
For me the flat neck profile of a Les Paul (even if it’s larger) is easier then the smaller curved neck of a strat.
I think the best option is: go to shops, play guitars where you’re interested in, and feel what’s best for you.
Where I live, (a small island in Thailand) you can ‘look but don’t touch’ the guitars in the shops. There is one shop that will let me play them, but they specialize in electric guitars, whereas I am still playing only acoustic.
That’s particularly stupid.
Worse than hifi shops that don’t let you listen to things
Fingerboard radius is normally less of an issue with acoustic guitars as they tend to have flatter boards - necks do vary quite a but though and I’ve had a lot a variation even with two guitars which should have been identical. Not letting potential customers play the guitars isn’t very sensible as @RobDickinson says.Perhaps if you do your research beforehand and go into the shop saying ‘I’d like to try these two models as I know they have a different neck and I want to see which suits me better’ you might have more luck? I can sort of understand a shop wanting to avoid people just coming in and playing a bunch of guitars with no intention of ever making a purchase - however this is part of owning a guitar shop!
I have bought three of my four guitars without playing first and have enjoyed them all. I am not that picky yet in my guitar needs. The more I learn, I may become more picky, certainly if I was going for a higher end instrument.
My point is that with research, you can probably do ok without playing first, avoiding guitars with outlier specs. Most neck profiles are pretty easy to handle, most neck radii on an acoustic will be pretty flat. Guitar size and scale length may be the features they are most important, assuming a good set up.
If we get to a point where the more obscure specs matter, then worry about it.
However, I agree that a brick and mortar store that won’t let you play the guitar before buying makes no sense at all. The only way to learn how different guitars feel is to play them and the only place to do that reasonably is a guitar store. Maybe it is different in Thailand, but here, if I can’t play in a store, they offer nothing to the buyer except immediacy.
Anyway, for acoustics, I would not worry at all about neck radius at this point. Electric, yes, worth thinking about how you want to play and either look at the rounder vs flatter, but I wouldn’t sweat the 7.25” vs 9” differences much.
Oddly, I have owned two electric guitars, now only one of them. The Carvin that I sold was notorious for its flat and fast fretboard with a 16” radius. I measured the old Westone strat I still have and lo and behold, 15”. Guess I lean that way…
You hit the nail on the head, as the saying goes. I am not yet to the point of needing a high-end guitar, although I have determined that because of my age I prefer small bodies as I find them less painful to play.
Where I live, while not entirely remote, is very tourist oriented. I think a lot of the tourists wander into the little music stores and want to play the instruments with no intention of buying, hence the owner’s reluctance to let anyone play.
In short, these shops are interested in selling to the local musicians, not to tourists. I am not a tourist, but I look like one (a foreigner) so it’s hands off the merchandise.
It is hot and humid year-round. I love it; but wood guitars not so much. I recently went on an extensive trip and when I returned months later one of my two guitars, parlor size, was severely affected, despite following recommendations to prevent it. So, I am giving up on wood guitars and looking into carbon fiber. But… yikes! The price!! That’s why I am looking into every aspect of what makes up a guitars ‘playability’ (less painful) before making an online purchase.
Look into Enya carbon composite guitars. The price may be more to your liking.