How to read different lines of a file to different variables?

You'd do:

{ IFS= read -r line1 && IFS= read -r line2; } < input.txt

Or:

{ line1=$(line) && line2=$(line); } < input.txt

(less efficient as line is rarely built-in and most shells need to fork to implement command substitution. line is also no longer a standard command).

To use a loop:

for var in line1 line2 line3; do
  IFS= read -r "$var" || break
done < input.txt

Or to automatically define the names of the variables as line<++n>:

n=1; while IFS= read -r "line$n"; do
  n=$((n + 1))
done < input.txt

Note that bash supports array variables and a readarray builtin to read lines into an array:

readarray -t line < input.txt

Note however that contrary to most other shells, bash array indices start at 0 not 1 (inherited from ksh), so the first line will be in ${line[0]}, not ${line[1]} (though as @Costas has shown, you can make readarray (aka mapfile) start writing the values at indice 1 (bash arrays also contrary to most other shells' being sparse arrays) with -O 1).

See also: Understand "IFS= read -r line"?

I'd offer to use array for such task(s)

mapfile -t -O 1 var <input.txt

so you'll have each line in ${var[1]}, ${var[2]} and so on

This is not strictly what you asked for, but it might work for your needs. You can serialize the data with Awk. Note that this will break if your $1 is not a valid variable name:

awk '
function quote(str,   d, m, x, y, z) {
  d = "\47"; m = split(str, x, d)
  for (y in x) z = z d x[y] (y < m ? d "\\" d : d)
  return z
}
{
  print $1 "=" quote($0)
}
' input.txt > /tmp/input.sh
. /tmp/input.sh

Result:

$ echo "$line1"
line1 foo foobar bar