Buy from a reputable dealer who has a "no questions asked" return policy. Remember, unless you are purchasing a synthetic, mass-produced drum, all drums made of wood and goat skin have a distinct voice. It's ok to purchase a drum on the internet as long as they provide clear contact information and have a good return policy.
Different woods produce different sounds. It's hard to know what type of wood you are going to prefer. This really just requires you to play a lot of drums. Some woods from Africa are very hard and subsequently very heavy. This does not mean they will sound better. In fact, I prefer a drum that does not weigh a ton. Lighter drums are easier to handle and thus you are less likely to damage them. Mahogany makes a very fine wood for drums. Mahogany is a relatively stable wood, does not weigh a ton and is dense enough to produce a nice open sound. This is why many drum set manufacturers build drum shells with Mahogany. Mahogany is also often plantation grown which is an important environmental aspect.
Be careful of some of the thin and/or two piece shells on the market. If they don't say their drums are made from a single piece of wood, don't buy it. It won't sound good and it's sure to crack sooner or later. Thin shells will not produce a good bass tone either.
Look for drums laced with Alpine rope and not just heavy string.
What should you listen for? Listen for open, deep bass tones and a nice sharp crack when slapped. Look for a drum that's easy to play. You should not have to use a full force blow to extract a nice tone. The drum should sound good or respond at all volume levels. The tone should have a nice sustain without strange overtones or pitch shifts/bends. If you do encounter these symptoms, they can sometimes be corrected with tuning. They can also be the result of a poor quality head or an uneven bearing edge. If it's just a tuning issue, you can sometimes test this by placing the drum on the floor, holding it down with one hand, striking the drum and pulling up on the lacing. If the pitch evens out or improves, it's likely just out of tune. Another trick is to place a heating pad on the goat skin drum head at low setting for a few minutes. This may bring the pitch up enough to take out the overtone.
The best thing you can do is just make sure you are dealing with a reputable dealer with a clear return policy. As with many other products, there are plenty of people out there buying large quantities of cheap drums and dumping them into the market.
You don't need to spend $350.00 or $400.00 on a drum to get started and learn how to play. However, you generally get what you paid for. Good drums that you will enjoy playing for the rest of you life start at $250 and go up to $750. I peasonally don't see the difference in drums past $750.