Corded drills are good for quick drilling jobs, but they are heavy and require a nearby electrical outlet or extension cord, making them less convenient. My old, cheap corded drill is extremely barebones and lacks a lot of essential features. For example, it does not have a clutch or keyless chuck, and the only speed control is in the trigger. Nicer drills will have a switch that toggles between a slower "driving" mode and a faster "drilling" mode.
Cordless drills are much more convenient--but only if you buy one with good battery technology. Avoid NiCd/NiCad (Nickel Cadmium) batteries, as they charge slowly, commonly have an annoying "memory" problem if you don't maintain them properly, and will never be ready to use when you want to use them. Trust me, you won't want to have to charge your NiCd batteries for 4-8 hours every time you want to use your drill. Instead, buy a cordless drill with a NiMH or, better yet, Li-Ion (Lithium Ion) battery. Preferably, buy one with two batteries and a quick charger, so you can charge one battery while using the other, and you'll be much less likely to get stuck sitting around idle waiting for the battery to charge.
For a novice or home user who will only use the drill a couple times a year, I'd recommend a cheap Lithium Ion drill with 2 batteries for $50 or less. Again, DO NOT buy a drill with NiCd batteries. It will serve you well for several years if you store the batteries inside your house and avoid subjecting them to extreme temperatures such as a garage that gets below freezing in the winter.
If you plan on building things or using your drill more frequently, your first set should be a 12v compact drill/impact driver combo kit from a reputable manufacturer. You can usually find these on sale for $100 or slightly more. The greatest advantage is that you won't have to constantly swap between your drill bit and your screwdriver bit. The bonus is that an impact driver is much less likely to strip your screws, even with a Phillips screwdriver bit.
Other important features for a drill:
- keyless chuck
- self-locking keyless chuck (so the chuck doesn't try to spin while you're trying to tighten it)
- clutch (so it stops trying to drive the screw once it's torqued a certain amount)
- light (so you can see what you're drilling or driving)
- onboard bit storage (sometimes it can be a bit gimmicky
- magnetic bit/screw holder
- speed control (a switch that converts between faster "drilling" mode and slower "driving" mode)
- forward/reverse (included on all drills I've ever seen; cordless drills also typically have an "off" position that locks the trigger during transport)
- multiple batteries
- battery charge indicator (either on the drill or battery; sometimes branded as a "fuel gauge")
- 1/4" hex chuck or adjustable chuck (impact drivers usually have 1/4" hex chucks)
- swappable driver heads--offset, impact, right-angle, normal, or other
- battery compatibility with many other tools
- extended-life or slim battery options
- carrying case or bag
- belt clip
- higher torque (impact drivers have much higher torque than drills)
Drills, like many other tools, are commodity items these days. In short, you get what you pay for. The more premium brands typically offer better battery technology (faster charging, better able to hold a charge between uses, batteries that continue to hold a charge after many years of charging cycles) and more features, although some homeowner-targeted brands do include extra features.
On top of the features above, you can also purchase different types of drills such as hammer drills and rotary hammers and drill presses, which address more specialized needs. Because this question is more about recommendations for a novice, those other types of drills are outside the scope of my answer and would be better served by separate questions.