Wow question I'm qualified to answer since I have this computer and have done a ton of research on the CPUs for it . The board is socket 775 but there is publicly available modded bios to run lga 771 if you use an adapter or buy one with an adapter pre-installed from ebay or aliexpress that will make that board support a Xeon X3 line processor. Now there are good Xeon X5 lines as well but from what I found you would need an optiplex 760 to run those on the modded bios. Im not positive an X5 line like a Xeon X5450 couldn't work but I didn't want to risk it since it was a long shipping time from china.
As for what processor you should buy I would say your best options listed are here listed from highest to lowest price:
These can all be found for the ranges of 5$-45$ and are your best choices without spending too much or going too low on performance. For reference you can see a full list of these performance on 775/771 processors here:
On mine I have a modded Xeon X3363 which is 2.83ghz quad core with 12mb L2 Cache. I got it on aliexpress for 10$ using a new user coupon for 4$ off. Prices seem up right now about 5-9$ higher than I ranges I was looking at last year but they do fluctuate so I would expect they come down a bit depending on when you shop. Here is my full system for reference (needs a gpu upgrade :O):
20$ Dell Optiplex 780
10$ Xeon x3363 processor 771>775 Mod (4c/4t 2.83ghz)
45$ 16gb Hynix DDR3 1333mhz
25$ Intel 240gb SSD
20$ GT 730 2gd5
win 7 64 bit professional
Total cost : 110$
Also though it may risk make everything else I've said invalid but I think you can do better than the option you listed. Optiplex 760-780 are routinely available for very cheap on craiglist as many offices are getting rid of them and unless don't have an OS and don't plan on upgrading any other components this is not a great deal overall when base optiplexs are around for 20-40$. Also for 169$ you can probably find a slightly less old office machine running an i5 that would be far more capable. Techyescity also have done a lot of videos about the slightly newer (2010) 6 core xeons that can be had for very cheap on old machines: https://www.youtube.com/watch?time_continue=2&v=VMbUXKsMKKA
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