I'll preface this by pointing out that I am very much a Seiko fanboy, and that the heart of the watch, not it's dial, is what makes a watch interesting to me. Further, ultimately,
you are the one who is going to be wearing it, and thus
you should decide what you want. With that out of the way, here's what I think.
Hamilton is a nice brand. They have attractive designs. They use Swiss movements, which I believe is a modified ETA 2824-2. Rock solid, ubiquitous movement. Unfortunately, that is about all that can be said about the Hamilton. It looks nice and has a decent movement.
The Seiko on the other hand, uses a quirky movement that is quartz based. So if accuracy and durability are important to you, this is the one you want. However, as RBR pointed out, it is not just a quartz movement, it is one that has been designed to derive power from a rotating weight (an idea borrowed from mechanical movements, such as the ETA above) so that it never needs a battery. In a way, this is probably the best kind of movement for a watch, since it does not rely on a battery
or a main spring. It offers the durability of a quartz with the longevity of a automatic mechanical. As long as you always wear it, it won't need servicing until the bearings wear out or the gears crack. Another good one to look out for are the solar-powered watches that Seiko (and Citizen) offer. They look like ordinary watches -- no ugly solar cells visible -- but still require only light to run. Here is the SNE095P1:
Seiko's Kinetic Drive is used in
many different models. Jomashop, for instance, or Long Island Watch, carries a selection of watches based on this technology. Amazon, and Creation Watches as well. It is simply a matter of finding a style that suits you.
As an aside, the style of watch you are looking for is typically referred to as a "field watch," which just means a simplistic format with maybe a date and a center seconds.
In an addendum to the above, I adore mechanical movements. I feel they have much more
character and interest than quartz. If that is the route you want to take, you can invest in any of Seiko's mechanical movements as well. For instance, I own a Seiko Alpinist, with the green dial, which is not merely accurate and useful, but simply gorgeous as well. I can't praise it enough:
The gold and the green go fantastically together, and I often find myself staring at it, mesmerized for a moment, while washing my hands or eating. Of interest is the inner rotating bezel; the crown at the 4 o'clock position, when turned, makes the inner ring (which is marked like a compass) spin in either direction. In this way, you can use it as a solar compass, if you so chose.
Another interesting manufacturer that I've begun to explore recently is Vostok, specifically the Amphibia line. It is a fascinating piece of Soviet engineering, and I am happy to have one in my collection. I do warn you, though, the dial styles tend to be.. esoteric. The movement is renowned for being utterly bomb-proof, however.
Many of my watches tend towards the "diver" style. I think you'd like it -- just hours, minutes, seconds and sometimes a date. Seiko has many watches in this realm, as well (surprise) ranging from the "Orange Monster" to the "Baby Tuna" or even the "Shogun."
I'll stop here lest I go on too long. I will say in parting that the most important part is to find something
you like. You'll be wearing it, staring at it, and in the end, that is the choice that matters. Most mechanical or quartz movements are going to serve you perfectly, so don't worry too much about what's inside, unless you're like me and are a nut for gears and springs.