I'd suggest getting the largest type that works for your application, purely for mechanical stability. The common mini-grabbers are great for DIP and decent for SOIC, but I wouldn't use them for anything with a finer pitch than SOIC. They are not so great for large components like TO-220 (possible ground connection). There are larger grabbers like mini grabbers for that, but they are not often used with logic analyzers. For smaller pitches there are smaller grabbers, but these are much more fragile.
This page on the Sigrok wiki gives a decent overview. In my opinion it is worth paying for quality (e.g. EZ-Hook) over the cheap Aliexpress crap.
As far as signal integrity, any sort of extension introduces inductance and degrades signal integrity, but I'd expect bench top analyzers to be less sensitive due to their lower input capacitance because of the resistive divider near the tip and lossy cables they use, while USB analyzers usually have much more basic probes, like a bunch of unshielded "dupont" wires. But this is not generally the reason for the manufacturer to omit them, that will be purely a costs saving.