Almost every watch you'll look at is one of two things: automatic or quartz. Understanding the difference is the single most useful thing when choosing a watch, so here's the plain-English version.
How an automatic watch works
An automatic is a mechanical watch that winds itself from the motion of your wrist — no battery. A weighted rotor spins as you move and keeps the mainspring wound. Wear it regularly and it keeps running; leave it off for a couple of days and it stops, then restarts with a few shakes or a wind of the crown.
The appeal is the feel: a smooth, sweeping seconds hand and the sense of a tiny machine living on your wrist.
How a quartz watch works
A quartz watch keeps time with a battery and a quartz crystal. It's extremely accurate — seconds a month — and very low maintenance. The trade-off is the once-a-second tick instead of a sweep, and a battery to change every so often.
Head to head
Accuracy: quartz wins comfortably. An automatic runs within a range of roughly +/- 20–40 seconds a day, which is normal for a mechanical watch.
Maintenance: quartz needs the odd battery; automatic needs no battery but benefits from a service every several years.
Feel: automatic wins for character — the sweep, the self-winding rotor, the mechanical heart.
Cost: quartz is usually cheaper to make; a good automatic costs a little more but gives you a real mechanical movement.
The middle ground: Meca-Quartz
There's a hybrid worth knowing about. A Meca-Quartz chronograph keeps time with quartz (accurate, low-maintenance) but uses a mechanical module for the stopwatch, so the chronograph hand snaps back with a satisfying mechanical action. It's a great option for a sporty chronograph — more on that in What Is a Meca-Quartz Chronograph?
So which should you buy?
Choose automatic if you want the soul of a mechanical watch and don't mind winding it now and then. Choose quartz / Meca-Quartz if you want maximum accuracy and minimal fuss, especially in a chronograph.
At COSO the automatic lines run on the Seiko NH35, and the Torvex chronographs run on the VK63 Meca-Quartz. Not sure which suits you? Build your own COSO or read NH35 vs VK63.