A remake is a waste of valuable time and resources. The trilogy is still playable, and fun today.
However, if you held a gun to my head and made me pick a game to remake, this is the one I would go with because I think the vision there is phenomenal and unmatched. The characters are great, the art design is the best in the series, the OST is the best in the series, the battle system is fantastic as well.
I think it's one that didn't reach it's full potential due to 1) PS3 being a nightmare to program for, 2) being the first major HD game they made, and grappling with that difficulty during development.
They could easily remake it with more open areas and numerous towns like we saw in XIII-2, or VIIR-2. Battle system could build on XIII and VIIR content as well. Just do the 1st game, even though the whole trilogy is great that's just too much.
My top choice though is to not do it and just make a new game.