Again, not sure why the COUNTIF formula is not:
=IF(C20="","",COUNTIF($C$3:$C$2000,"<="&C20))
I'm assuming this formula is in column B
But your 2nd formula needs to callout entire column within the SMALL function would be:
=VLOOKUP(SMALL(B:B,ROW(A1)),$B$3:$C$2000,2,FALSE)
Copy this down as needed. Note that I modified Chandoo's formula by using the ROW function so that it automatically chooses the 1st smallest, then 2nd smallest, etc. Also, since the first formula is already sorting out the blanks, that part of the formula is not needed.
Making a large guess, if you're needing to do the VLOOKUP to pull in other data besides the sorted list (say, you sorted names, but also want to have additional columns sorted), we need an extra helper column with this formula:
=RANK(B3,$B$3:$B$6)+COUNTIF($C$2:C2,C3)
Again, this assumes that col B has the first COUNTIF formula. Now, change the VLOOKUP formula to reference this new helper column (I'll assume you used column A) like so:
=VLOOKUP(SMALL(A:A,ROW(A1)),$A$3:$C$2000,3,FALSE)