You can't do that kind of subsetting with $. In the source code (R/src/main/subset.c) it states:
/*The $ subset operator.
     We need to be sure to only evaluate the first argument.
     The second will be a symbol that needs to be matched, not evaluated.
  */
Second argument? What?! You have to realise that $, like everything else in R, (including for instance ( , + , ^ etc) is a function, that takes arguments and is evaluated. df$V1 could be rewritten as
`$`(df , V1)
or indeed
`$`(df , "V1")
But...
`$`(df , paste0("V1") )
...for instance will never work, nor will anything else that must first be evaluated in the second argument. You may only pass a string which is never evaluated.  
Instead use [ (or [[ if you want to extract only a single column as a vector). 
For example,
var <- "mpg"
#Doesn't work
mtcars$var
#These both work, but note that what they return is different
# the first is a vector, the second is a data.frame
mtcars[[var]]
mtcars[var]
You can perform the ordering without loops, using do.call to construct the call to order. Here is a reproducible example below:
#  set seed for reproducibility
set.seed(123)
df <- data.frame( col1 = sample(5,10,repl=T) , col2 = sample(5,10,repl=T) , col3 = sample(5,10,repl=T) )
#  We want to sort by 'col3' then by 'col1'
sort_list <- c("col3","col1")
#  Use 'do.call' to call order. Seccond argument in do.call is a list of arguments
#  to pass to the first argument, in this case 'order'.
#  Since  a data.frame is really a list, we just subset the data.frame
#  according to the columns we want to sort in, in that order
df[ do.call( order , df[ , match( sort_list , names(df) ) ]  ) , ]
   col1 col2 col3
10    3    5    1
9     3    2    2
7     3    2    3
8     5    1    3
6     1    5    4
3     3    4    4
2     4    3    4
5     5    1    4
1     2    5    5
4     5    3    5