Thanks to everyone for the feedback. So far the TL;DR I get from all the responses is:
"Expensive probes are kinda nice and can make a difference but probably are not really worth the money, cheap or diy ones do the job at a fraction of the cost."
@mawyatt that is a nice collection of probes you have there, also thank you for posting your test measurements, the probes you tested all seem to be pretty good. The most impressive were of course the single shielded ones tested on the DMM6500. It would be interesting to see a comparison where you swap one of the probes you tested with the KS with those tested on the Keithley just to see if the probes are that good or if it is the DMM or a combination of both.
You may already know this, but you don't need Kelvin clips to do a four-wire (Kelvin) measurement. It works pretty much as well if you use four separate wires. The only downside is the extra hassle of having to attach four clips, and possibly extra noise pickup unless you twist the wire together (sense with sense, force with force).
Yes thats a good point using four seperate clips/grabbers and not touching the probes is surely the best way to go in many cases. There is at least one case where Kelvin probes, especially @JohnGs
Pomona probes are really useful (IMO): Following the lowest resistance path to trace a short. With regular two wire probes your test leads keep influencing the measurements and may send you on a goose chase, but with these 4-wire-2-point probes you pretty much eliminate the effect of your leads. Tracing shorts with 4 seperate wires especially when SMD components involved is cumbersome . In the past I used my "poor man's version" of the Pomona 6303 probes, with varying degree of success. Here is a picture for the amusement of everyone around


While they don't perform actual 4-point measurements and thus may not give the most accurate absolute value they give pretty good relative measurements and eliminate any influence of the test leads. If anyone knows cheaper alternatives to the Pomona 6303 let me know.
@Electro Fan I was also looking at the BK TLDK1 and liked them but they are also rather expensive here. You can expect to pay 100€ in Germany.
@TomWinTejas, @duckduck: The AST probes look nice but don't seem to be easily available in Germany. Importing them from the US will make them a lot more expensive due to shipping + import fees.
@alm: I did a quick search on ebay for the Keithleys, the cheapest 5805s currently available are 172,93€ + shipping

. Maybe there pops up a bargain at some point.
@SHTechnics: I do like
the banggood ones you linked a lot, are affordable and also look like they are less bulky and more flexible than the ebay-GW-Instek ones I posted. I think I might buy a pair of these to give them a try.
@Hydron: Thanks for reporting back on your experience the GW-Instek ones I linked in my original post. Before you and alm mentioned it i didn't recognize how wide the clip-tips are. Indeed I was looking for something more filigree.