Quick question: I'm thinking of building my first AR, and I'm wondering if I need to get an ambi selector, or if I can just install the normal selector on the other side.

First off, don't listen to the naysayers that will tell you to just learn how to do everything like a righty.  The AR-15 was designed for right-handed personnel, hence the controls are ergonomically position for right-handed efficiency.  Sure one could learn how, but given the amount of time for this learning curb one could spend that extra time learning other fundamentals of shooting.  If it's a personal rifle, personalize it to you (and most of the lefty stuff is ambidextrous so it can be used right-handed as well).

That being said, I don't know the answer to your question...just trying to pre-emptively answer the responses you're going to recieve.

Installing the normal selector/safety on from the other side is not possible due to the detent and the "slots" in the safety.  IIRC, some company made a safety that did have slots to engage the detent when installed from the other side.  Or you could just get an amby safty and install it.

Put a DPMS Ambi on my RR.

Simply relpaces the selector switch with the right side lever held in key slot with an allen head screw.

I always wondered how the other lever was secured on besides the screw.  So it is solid right?  No chance of it coming loose?

I have 2 AR's built or customized by me for left hand use. Both have Ambi safeties and Ambi mag releases. Well worth it to me. One is a left-handed DPMS receiver . I love it, finally now I can lend it to a right handed shooter and let them see what I have to put up with. I have toyed with the idea of cutting the right side safety lever off. may still do it.

I haven't seen an ambi mag release, who makes those?

"I always wondered how the other lever was secured on besides the screw. So it is solid right? No chance of it coming loose?"

It's a solid mechnical connection with the allen head simply holding it into the slot on the main body of the safety's x-pin. Put mine on
with #242 "Blue" Loctite and it has yet to loosen at all. Think you'd notice it long befor it became a problem.