Capturing higher level slaves tends to result in them having higher grades, such as Rich or Noble, which have a higher range of starting beauty (each higher rank has an average of about +10 beauty). Slave rand can be raised later at the slaver's guild, but it will not change their beauty. Higher level slaves tend to come from areas that are further from major towns and thus have higher level enemies. The highest grade slaves are found in bandit camps, which can be rather difficult battles. Also, exploring the deeper regions of an area often results in finding slaves with 1 higher grade than usual, though there will be about 40% more enemies that will be about 30% stronger.
The beauty stat has many workarounds even if you capture a slave with slightly less beauty than you need. The laboratory operation and tattoos are the most obvious methods, but there are a few exploitative methods as well. The laboratory operation will give 30 if they have low beauty and 20 if they have high beauty. The nature tattoos will give 5 per tattoo, up to 15.