What are some major considerations for having an accurate ADC (SAR type)?
See this
http://www.delftek.com/wp-content/uploads/2012/04/National_ABCs_of_ADCs.pdf


Not directly. Of course, a bad buffer will ruin your digitized signal, adding noise, shifting or gaining slope, clipping, etc.
Of course, speaking about precision. If you have 16 bits and 3V reference, this means 3/2^16 will be 45.77uV. Any ripple more than this value will destroy your ENOB (effective number of bits). In other words, you will have 10 bits of your great and expensive 16 bits precision ADC.
Clock jitter will greatly impact performances as general rule of thumb. For Some external ADCs (SPI for example) clock is internal and not modifiable. 


The only thing to take care is jitter of start conversion (CS - chip select) which will impact sampling points precision over time and SPI clock (grabbing data) which in some cases must not overlap acquisition time but it's hard to say, just read particular ADC datasheet.