Method 1 : Answer key for Row 1 (161), Row 2 (23)

Method 2 : Answer Key for Row 1 (5), Row 2 (4)

Method 3 : Answer Key for Row 1 (1), Row 2 (1)

Method 4 : Answer key is ABCFED

Throwing an opinion.

How about describing the row/column by S (straight), T (turn, or bent/corner might be better), and U (unvisited, or empty)? Example for row 1 (UTTTSSSSSTTT) and row 2 (USSTSTTSSTSS). Inspired from my tendency to make things pretty consistent and Fillomino's widely-known answer key description (units digit of the marked row/column).

I am reminded of the recent HALAS League competition (http://sudokucup.com/sites/default/files/B_SubmittingInstructions.pdf - check Railway puzzle, page 19).

IMHO, we should avoid English letters that translates to something, unless it is a word puzzle like the ones in Word Show.

I (straight), L (bent), O (empty) then :P

Or maybe numbers (1 for straight, 2 for bent, 0 for empty for example) work.

But for large puzzles I prefer marking some squares and determining what's in it (ILO style too), or otherwise method 1 or 4.

I'm ok with letters only if they're required in isolation rather than entering a string. Maybe use A. B. C. like some of the Moscow Cup keys to ask whether a certain cell is I, L or O. I think you can pretty much cover the entire puzzle by knowing if say 5-6 cells have the loop passing through bent, straight, or not at all.

Sorry, what? I don't quite get what you mean here.

If I'm a solver, I'd rather enter just a letter for a cell (For example the Easy As Cup puzzle in the recent Moscow Cup) rather than entering a string of letters describing a row/column like for example UTTTSSSSSTTT. If you just circle/mark a bunch of cells, meaning I have to enter a letter describing each of those cells in isolation, you can cover the puzzle with 5-6 descriptive cells and its less work for me as I can just jot down the letter in small in the marked cell as I'm solving.

As we encounted in the USPC the other year, if you go with "letters in order visited clockwise", it's good to put the starting letter on the edge of the puzzle.
For example, starting from point F, mathematically "clockwise" would go upwards, but many folks would assume it went leftwards.