You don't need grep since you aren't searching for a pattern, you want line #3 (or line N).
To get line 3 you can output the first 3 lines from the file, then take the last line from those three:
head -3 filename.txt | tail -1
You mention backticks, so if you want to assign that, or output it, enclose it in $(...)
instead of backticks.
linethree=$(head -3 filename.txt | tail -1)
If the file is very large and the line N you want is far into the file it would be more efficient to use sed, such as
sed 4321q;d filename.txt
or
sed <n>q;d filename.txt
as outlined in this answer.