I say just walk the lands until you have pretty much mapped all the locations. Be warned, picking items up from chests and trunks and off bodies can and will break quests. Do all the easy ones first. The misc quests. Those are ones that often become abandoned and broken due to you already clearing out a cave/den/camp/thingy. If you find an item with a name, like " Hammer of Tanoman" then its probably a quest item. Also, if a book is in a chest don't take it. Don't even read it as you may accidentally grab it.
I'm not sure why this person wrote this. I've never had problems with quests breaking because of picking up items when you find them. This has literally NEVER HAPPENED in my game and I've been playing Skyrim on PC since the very first day it released. ... Well over 200 hours of play, and probably closer to 300. I've done the main quest twice, done the civil war quests twice (once as Stormcloak and once as Imperial), and done all of the faction quests (thieves guild, mage's guild, etc). Maybe they're playing on a console or something? I've heard there were/are more bugs with the console versions.
Well, I think at least the part about "don't pick up any books you find in chests" is good advice. I avoid doing that because I've read numerous posts (and on wiki) that if you pick up a book that later becomes the subject of one of the college orc's radiant quests you can't give it to him and therefore can never complete the quest. I haven't pressed the matter to verify personally, mind you. One of the first things I noticed in my current game was a book in a giant camp chest near Whiterun. Sure enough, much later on it became the first target for one of those book quests.
Maybe the book thing isn't correct but, yeah, I've read enough stuff about it that I take the "better safe than sorry" approach.
Having said that, I have looted a couple non-book that I couldn't sell or store and were (obviously) quest items, but I've been able give them to whatever NPC the items were associated with when I eventually found them to trigger the quest. Still, if I knew before looting that it was a quest item, I wouldn't take it just in case. Again, just better safe than... And, worse case scenario, you have to go back to the location once the quest is triggered. AND you don't have the annoyance of an unstorable item cluttering up your inventory. (I'm recalling accidentally finding that corpse of the missing husband before you're supposed to, and not being able to trigger that quest or get rid of the journal entry. Maybe no huge deal, but still...)
edit:
Go download steam mods ASAP , and DO NOT fast travel. Skyrim is made to be explored.
regarding Steam mods: not to discourage the OP, but I'd advise to take the time to understand how steam workshop works before doing that. In particular, know that Steam automatically updates mods when a new version is issued. Personally, I avoid them for that reason (and stick to stuff here on Nexus). Automatic steam updates for the game are, imo, bad enough. Automatically updating mods is, again imo, insane.