Once you become certified with OW (likely PADI), I would recommend not going below 66'. I admit, I went to 78' on my 3rd dive after being certified but it was with a DM as a buddy and the visibility was 300', where as my dive training at 60' had 3' visibility.
It's all in your comfort level, your buddy, and your training.
Once you dive more and possibly take more class, you should be able to go to 100' without much trouble. 130' is the recommended maximum depth for ANY recreational diver, and at most dive sites, there's not much to see past 130'. Some people do it for the thrill of going deep, but to me that sounds like medicine for a disaster. Right now I only feel comfortable going to about 110' when the rest of the conditions are good (visibility, thermal protection, etc.). I'm sure as I dive more I'll feel comfortable at 120-130.
The other thing to know is that the deeper you go, the more air you consumer. It's based on atmospheres, and every 33' is 1ATM. Thus at 66' you consumer twice the air that you do at 33'. At 33' twice the air as surface. Therefore at 99' you're using 3 times the air of 33', 4x the surface.
Your depth should be based on your "dive plan" (important word). What do you want to see down there? You should proceed to the max depth of your dive plan first, and slowly ascend up as you go through your dive. I prefer dives that are around 50-70' because you get good bottom time, nitrogen absortion isn't bad, and you can do repetitive dives without much concern. Most dive sits I've been to have had all of the things to see above 100' anyways.
Good luck, be safe, and have FUN,
BrianV
Also, remember that the pentalty for failure when scuba diving could be death!