I think this should have all the information you need. From that faq, these are the items that are suggested you not sell:
- Bhujerban Madhu (can be sold for 250, but the related sidequest nets you 1000 each)
- Black Orb (actually okay to sell, but only worth 1 gil each)
- Centurio Hero's Badge
- Dewdrop Pebble (no opportunity to sell these, actually)
- Great Serpentskin
- Jaya Stick
- Nebralim
- Pinewood Chop (classified as loot, but actually can't be sold)
- Sandalwood Chop (same as Pinewood Chop)
- Semclam Shell
- Small Package
- Teleport Stone (keep at least 10 at a time)
- Valeblossom Dew
As I recall, the great serpentskin was the only thing that wasn't immediately obvious that I might not want to sell it. In any case, even if you do sell it you don't miss out on anything permanently.
I don't recall any loot being necessary for the main storyline other than the pinewood and sandalwood chops, but as I noted you can't sell those anyway.