Start with the basics.
Start with a basic set of a four- or five-quart pot and a seven- or eight-quart pot, both with lids. These two are enough to cook most recipes.
Add to your collection.
Add one- or two-quart saucepans and a larger eight- to twelve-quart stockpot.
Get a handle on things.
Look for pots with sturdy handles. Since larger pots will consequently have more food in them, good handles are important. Select pots with riveted all-metal handles (preferred) or welded handles. Metal handles can get hot, but that's not a problem if you invest in some oven mitts, and it's better than the handle coming off in your hands. "Cool" handles are also available.
When in doubt, go stainless.
Consider stainless steel pots to start a basic set. Stainless steel is relatively inexpensive and will not react with acidic foods the way aluminum and iron will. The downside is that stainless steel pots tend to be thinner, which means they get "hot spots" and can burn food more easily.
The heavier, the better.
Look for thick-walled pots with heavy bottoms. These will heat more evenly.
To stick or not stick?
In general, you're better off without non-stick surfaces in pots. Most of what you'll cook in a pot isn't at risk of sticking, and many recipes require the vigorous use of tools like spoons and whisks. Over time, even wooden and coated utensils will wear down a coated nonstick surface.
Review your budget.
Check your bank account: if your budget permits, choose top-quality pots with aluminum or copper exteriors for the most even heating and stainless interiors for non-reactive cooking. "Anodized" aluminum is treated so it won't react with acidic foods.