How do I tell what spindle length to get for a single crankset to use with an internally geared hub? I know that I need to maintain a correct chainline, so do I just measure the width of the hub and buy the same spindle length for a square-taper crank? Thanks.

It depends on the crank set and what the chainline of the hub is. IGHs that use 3 spline cogs have around 5mm adjustability as you can flip dished cogs around, or run a non dished cog as required.
I've done a large number of conversions, and have always managed to zero in on correct chain line using a combination of cog flipping or axle spacers to move the chainline one way or the other, and square taper BBs at the short end of the spectrum, like 107 or 110 mm.

It's a Shimano Nexus 8 speed hub. I haven't purchased the crank or the BB yet, I wanted some advice first. So should I be on the lookout for a single crankset that will pair with a 107-110 mm spindle BB?

That hub has a chain line around 43 mm if I recall. If you are buying a crank, hopefully the seller will have the specs on spindle length for specific chain lines, but having bought lots of generic cranks myself, even from distributors, that info is not always available. Sometimes it's trial and error.
I think the 43mm is with the cog dished in, so you can always go wider and dish it out.
And while perfect chainline is a laudable goal, the truth is it will work just fine if it's off a few mm.

Variables, : Hub Chain-Line (where the sprocket is relative to bike centerline)> crank choice >
whether you want that 1 chainring on the outside position of the double Crank , or inside with a trouser guard ring on the outside .

All I can say is what I use, but Hub is R'off , crank is an M730 and I use the disc on the outside position (& frame has MTB tire clearances ) then it is a 127.5.