A bit more to add regarding the protection diodes... The BAS116 is about $0.25, and has 5-10nA of reverse leakage current.
The diode connected 2N4117A has up to 200fA leakage at Vgd around -20 to -25VDC ..depending on where your signal ranges are set, then your max signal might actually be lower than this, and the leakage could be as low as 150fA @ Vgd -10VDC . It's a great part, but the 2n4117 is extremely expensive and mostly non-stocked. I might consider a purpose made low leakage diode before I chose this part, unless I absolutely needed it's fA leakage (like in a 7.5 or 8.5 digit meter)
Finally, the much cheaper jelly bean 2N3904 BJT has a typical reverse leakage of between 30-50 pA, and can go as high as a few hundred pA. These are nice because they are available as MBT3904 in a TSSOP-6 or SC70-6 package for $0.25 so you get two on the same die with similar leakage for $0.12 each.
The MBT3904 is what I am using for my LCR. I also happen to have many around here so they are readily available to me. Depending on your leakage budget, you can use them as is with an expected leakage max of 200pA (if that works for you) or you can bin them and choose parts with 10-20pA, an order of magnitude smaller.
I use a 1k input resistance, then the MBT3904s, then a 100 ohm, then the opamp input buffer. The 200pA max leakage across the 1K series input resistance is 200nV error max, and you can bin for less. I use a 24bit ADC with a 1.00V reference, so 1 LSB is 60nV, and this error is > 3LSB but that's ok for me, I only want 22 bits, so I can accept 4LSBs error. If it turns out that I have other error sources elsewhere that I can't control and blows my error budget, then I can bin the MBT3904s for better than 60pA leakage, or 1LSB and bring it back under control.
No matter what, the cheaper 2N3904, even if you use it in a TO-92, is much better than the BAS116 diode.
Cheers!