|A shavette - a type of straight|
razor that uses disposable blades.
A straight razor requires skill and care to use - careless use can result in serious injury. Keeping the blade at a good angle (something like 30 degrees) is essential for good results. This can be a challenge sometimes even when you can see the shaving area (as when you shave your face), but shaving the scalp is even trickier. While it can be done (and you can find videos on YouTube of people using straight razors on their scalp), I don't recommend them for shaving your head.
Though the DE safety razor has a guard in place to prevent big gashes (making them considerably safer than straight edge razors), they do require some care and skill to use. The blade still needs to contact the skin at a good angle, for instance. Traditional wet-shaving enthusiasts usually recommend a multi-pass approach, shaving first with the grain, then across the grain (and sometimes against the grain) for a very smooth shave.
You can certainly shave your head with a DE razor (I've done so in the past), but it's not something I recommend unless you're interested in the challenge and experience of it. While you're learning, it's pretty easy to draw blood, and it's fairly time-consuming if you want a smooth shave - it wasn't uncommon for me to take 30 to 45 minutes, and that was after much practice and effort.
The razor you're most likely to see advertised in contemporary media is the cartridge razor. The current champion (in terms of TV time) is probably the Gillette Fusion ProGlide, but there are many, including Gillette's Trac II, Atra, Sensor, Mach 3, Schick's Hydro and Quattro, and various generic versions of these razors.
The great innovation of the cartridge razor is that it holds the blade at a fixed angle relative to the position of the cartridge, and that it holds the blade at a fixed distance to the skin. This essentially reduces the skill required to shave, and makes it possible to shave more quickly and with less chance of nicks or cuts (though it is still possible to draw blood; you should never be careless with a sharp blade). Some models have a fixed head, but most have a pivoting head that changes position for you as you move over the curves of your face and scalp.
Another popular shaving option is the electric shaver. Unlike the other types of razors mentioned here, electric shavers can be used without wetting the skin, which can be very convenient. Their design also generally precludes nicks and cuts, though some people do find electric shavers irritating on their skin.
It's easy and safe to use an electric shaver on your scalp. I spent most of the past 3 years using one as my primary shaving device. The only downside is that electrics generally do not shave as close as a blade razor. I've tried a number of different models over the years, and while you can get a pretty close shave, it's never quite as smooth as I really prefer.
When all is said and done, I recommend the cartridge razor for headshaving. They are easier and quicker to use than straight or DE razors, and they shave closer than electric shavers.
The question of which cartridge razor to use? As with many things, it comes down to personal preference. I've used quite a few razors over the past decade-and-a-half of shaving my head, and I can honestly say that almost all of the cartridge razors I've used are capable of giving you a good, close, comfortable shave. Use whichever one you're already comfortable with.