The difference between 4hi and 4lo is 4hi connects the transmission to the front and rear axles in a 1:1 ratio which is direct drive. No reduction, its made for higher speeds. 4lo is a gear reduction to both the front and rear axles of 2.72:1. It gives you more torque and is much easier on your transmission when going through low traction situations. It is also meant for lower speeds. I figure since it was packed sand beach, the front driveline would bind a little and that would cause your Jeep to buck. That's normal. Just don't use your 4wd on dry pavement.
As far as tires you could fit a 32" without a lift but you'll have some clearance issues if you ever flex your Jeeps suspension. Much worse with 33" tires. You're going to need a lift for 33's unless you want to really hack your fenders to make them fit... which you won't. Your street tires will be fine. If you find yourself digging into the sand and losing traction, just air your tires down to a pressure between 15-20 psi. It allows the footprint of your tire to spread out over a larger area giving you flotation on top of the sand. It also works in really deep snow.
You can drive straight, you can turn just don't take a high speed turn with your tires aired down or you run the risk of popping the bead of the tire off the wheel. As far as going to the 4wd portion of the beach, go for it.
If you get stuck, I am sure other fellow wheelers would be more than willing to help you out. That's how you learn, is by getting stuck. We all get stuck sometimes. Other than that just have fun with it and don't forget to air up your tires once you are done playing in the sand.