Thieving is good if you don't want to waste time on every chest/door. I had it on third rank in act1 and there were barely few things that i had to force open. But you also need high perception (with Light spell preferably) to discover and disarm traps before you open lock.

Haven't used rest. I will try magical attack (which you didn't mention) when i'll have points to max it at once. Lower levels cost too much mana per shot.

So I succeeded in picking/looting the chest at the inn at rank 3 thieving. I'm not sure if it was the extra ranks that kept me from getting caught or if it was the fact that this time I noticed the chest was trapped and I disabled it first. :P

Thanks to Lothar's feedback, I think I've managed to find the things needed to open chests in the city.

According to my tests, chests work like this: You need to pick its lock first. To do that, Thieving skill is obligatory to have (and a high one at some chests). If you manage to pick it, the second phase comes, which is trap disarming (if you are not able to disarm it, an alarm sounds and a guard comes to arrest you.). High Perception is the key here (I tested by drinking Potion of Perception). If you disarm it successfully, the contents are yours and everyone leaves you alone.

Note that even with 20 in Perception, you can't disarm the trap if you did not pick the lock first. I tested it by drinking the perception potion around the chests that are too hard for me to lockpick. Trap didn't get highlighted (red). But I had managed to pick the chest's lock (in the inn), and by drinking the potion, I was able to disarm its trap since it was highlighted.

If you don't have Thieving and Perception, the only option to open them, as you know, "bashing". But in this case, the alarm is sounded when the chest is broken open and a guard comes. Maybe stealth helps here, but I have not tested it yet.

Hope this helps :)

Update: Picking the lock first is not needed to spot the trap. In a cavern, my char saw the trap first. I disarmed it. And then picked the lock on it. Just to let you know..