My league is having trouble deciding this, how does your league do it? I think it should just be reverse order of how we finished since 10 of 12 GMs are returning. Also, do yall do it at a house or go to a sports bar? It's time to get some draft talk going!!
I think random works just fine. Luck of the draw. It isn't about what spot you end up in. Especially this year.
I don't think the previous order should matter at all. In the leagues I've commish'd and in which I still take part, it's first randomize the order three times, then the picking order is one of the two: Pick 1-10 in 1st round, 10-1 in 2nd round, 1-10 in 3rd, 10-1 in 4th, and go that way until 8th round. Let the rest be random. We do this manually. OR Let the Yahoo! or ESPN or NFL league randomizer pick the players for you. In either case, PRE-draft players according to your likings, and if lucky enough to have them available, they'll fall to you.
I think it matters when there's keepers. If you keep the best player in the league there's a good chance you were a top team, then if you luck into the #1 pick, I feel that's unfair.
Random if your in a standard draft but if you are in a dynasty league, you have to go by record of previous season. IMO