When I first started climbing, I did only bouldering. I should think that is the logical manner to begin, for, when not yet certain if one will indeed take to this extreme sports, anyone with half a brain should know it isn't wise to invest in gear. A pair of reasonably-priced beginner shoes was the furthest I'd gone.
About six months into climbing, I got my own harness, ATC belay device and carabiner, and started top-roping regularly. It was a fortunate thing for me for having learned most of the basic stuff on the bouldering wall, for it afforded me more focus on overcoming my fear of heights (altophobia) and fear of falling from a high place (bathophobia) while top-roping.
A side note: I haven't come very far in those aspects... at present, I'm still scared, though at a relatively lesser degree.
Several months into top-roping, I was introduced to lead climbing. That was about a year and a half ago. All the while, for all the climbs, I used the ATC belay device.
An odd side note: ATC stands for Air Traffic Controller, and I have no idea why.
With the ATC, the belayer has to be on the alert, and focused on the climber all the time. If the climber takes a fall, his life will be, literally, in the belayer's hand. The right hand, in my case. Assisted-braking belay devices, on the other hand, have mechanisms to stop the rope according to the direction of the rope being pulled. The arguably most well-known of these is the GriGri (or now, GriGri 2) by Petzl. But no, we didn't get that.
We got Trango Cinch. I've never the opportunity to use a Gri Gri so I cannot fairly or accurately compare them both.
The Cinch is easy to use - the rope is enclosed inside, the climbing and belaying ends clearly marked.
The first time I used it I belayed a lead climber under the watchful eyes of an expert climber. As is the case with any new gear, it took some getting used to. For me, it was mainly the feeding - it took me several runs belaying for lead before I managed it fully smoothly and stress-free.
The "automatic locking", once the braking mechanism is set in, means the climber's life no longer rests in the hand of the belayer alone, although climbing safety rules dictate that the belayer should not let go of the free end of the rope at any time. Well, in case the belay device fails.
To be honest, though, the chances of the device failing probably will not be higher than that of the belayer panicking and letting go of the rope (during an unexpected fall), so I do think using the Cinch is safer than the simple ATC. Having said that, however, I also think it is important for new climbers to start off with ATC. I felt that the responsibility that came with using it trained me to really pay attention to the climber - not to take my eyes off him while he's climbing (as opposed to resting on tightened rope), and not to be distracted by sudden loud screams from the far corner of the climbing gym or a great-looking shirtless climber passing by... that sort of things. This sort of focus, I believe, is crucial, regardless of the type of the belay device used.
I don't believe I had ever posted so many photos of a single piece of gear here... this baby is just so pretty!
Climb safe, and don't take anything for granted.