There wouldn't be an advantage logging in at certain time, and a fairly small advantage, if any, logging in each day. Let's try this scheme.
Week 1, Day 1 The 48 players are revealed, showing their face, age, height, and best position. Teams have one week to choose 1 skill of 4 different players that is to be revealed.
Week 2. Day 8 One skill of 16 players is revealed to all owners. The teams have a week+ to set their draft order. Each team will have a draft time, 12 hours apart, at which time they will draft the top player on their list. So if you have the 3rd pick, you would only have to rank 3 players, in case the first two teams take the top 2 picks. Perhaps teams could also rank the positions (C, PF, etc), which would be a backup in case some one doesn't want to bother ranking a bunch of players.
Week 3, Day 15 Every 12 hours another player is drafted, and at the same time one additional skill of one player is revealed. Owners with upcoming picks can re-arrange their picks, or include some others in case their picks are being taken. But there really isn't much advantage, unless you ranked too few originally.
Week 4, Day 23, Start of 2nd round. The draft speeds up to one player every 8 hours.
Week 4, Day 28. Start of 3rd round, with one pick every 8 hours/
Week 5, Day 33, Draft is complete.
So the key times would be you 3 draft times. But you wouldn't have to be online. It might help to be online a bit before, just so you can react to other teams picks.