What kind of road bike wheels do I need to replace my stolen ones? I am looking to buy a pair of second-hand wheels, to replace a pair that was stolen off my 2012 road bike, but I'm nervous about compatibility.  I'd like to ask how exact I need to be in the following areas:


I believe (but am not 100% sure) that the old wheels were marked "622-14", which I guess means the rim width is 14 mm.  Do I need exactly this rim width?  I have Shimano BR-R560 rim brakes, but the manual for these does not specify what range of rim widths they will accommodate.
The cassette was a Shimano 105 10-speed, 11-28T.  Do I need this exact make, brand, number of speeds, and range of cogs?  I'd guess I should stick with Shimano and 10-speed, but there's no need to stick with the 105 brand or 11-28T?  However, that is a guess.


Is there anything else I am forgetting?

I'm aware of hub widths front and rear, but I've read that these have been standard on road bikes at 100 and 130 mm respectively for a long time - please do correct me if wrong!
Your hub widths are correct for non-disc wheels (disc rear wheels are 135 mm). 

You need a non-disc road wheelset with a 10-speed hub which is Shimano/SRAM compatible. Your cogs need to be a 10 speed set from Shimano or SRAM, and you want to have similar gear sizes. The particular set of replacements will depend on what rear derailleur you're running (which will set limits on the max cog size and a few other things). 

The rim width doesn't have to match exactly, but should be matched (roughly) to what size tire you want to run. See Sheldon Brown (or any of a variety of other sources, e.g. the Schwalbe website) for a table of what rim widths are good with what sized tires. These aren't hard and fast rules, but if you exceed them grossly, you may have issues.