Hybrid bikes are the perfect option when budget allows for only one bike.  The rider has a choice of road-oriented or mountain-oriented models, and women's-specific models are also available.  Since hybrids aren't specialized bikes, they have the capability of doing just about anything.  Choose the mountain-oriented models if you will be spending time on gravel roads or dirt trails. These hybrids have mountain gearing (fairly low), mountain bike wheels and tires, and may have front suspension.  They are not suited for difficult, rocky, technical terrain, however - they are not durable enough for that kind of abuse!  They are also quite heavy, which makes climbing hills more difficult.

schwinn-hybrid-700c-wheels

For road-oriented use (that is, mostly pavement with a gravel road or two thrown in occasionally), choose a road-oriented hybrid with larger wheels and narrower tires.  The emphasis here is on smoother, faster rolling, and it's not uncommon to see these types of hybrids on long rides, even centuries (100-milers).  Gearing is higher than on mountain hybrids, but the handlebars and shift/brake levers are the same as mountain hybrids.   

As comfortable as they are, road hybrids are not nearly as fast as road bikes.  Time trialing with hybrid bikes is not recommended because of the weight and relative slowness of this type of bike (vs. a road bike or a time-trial bike).  Other than using road tires which are inflated to a high pressure, there is not much that can be done to make a hybrid faster.  However, for someone doing a casual type of race, it's possible to modify the bike slightly to emphasize speed:  replace the wide saddle with a narrower saddle that allows for optimal pedaling efficiency; lower the handlebars so they are (if possible) a few centimeters lower than the level of the saddle; and switch from platform pedals to clipless pedals, which greatly improves pedaling efficiency.  Ultimately you'll have to work much harder than a rider on a road bike to time-trial or do a long road ride on a hybrid - but it's possible, and with a few modifications, not a bad compromise.

A quick guide to hybrid road bikes: start with the big manufacturers such as Trek and Specialized; they have a great selection of road hybrids from very, very casual to more performance-oriented (much lighter frames and lighter components).  If the emphasis is on speed and comfort, be sure to look at true road hybrids rather than very upright, heavy bike-path hybrids. 

A quick guide to hybrid mountain bikes:
again, the best place to start is with companies such as Trek/Gary Fisher and Specialized.  If your emphasis is on mountain hybrids, both companies offer alternatives to heavy, sometimes clunky bike-path hybrids.