There is one airport on St. Croix, Henry Rohlsen, formerly Alexander Hamilton airport.  If your plane comes direct from the states, baggage should not be a problem.  Except it takes a little longer to to get bags from the plane to the belt on St. Croix than most places in the world.  And that's with one plane; two on the ground at one time.....  Also if you connect through San Juan, there is a  50-50 chance your baggage won't fly on the same plane as you.  This is especially true of American/American Eagle.  

There is no immigration or customs inspection on arrival.  There are a couple of on site car rentals but you are better of dollar wise using off site car rental companies.  They pick you up at the airport.  There are plenty of taxis available just outside baggage claim. 

The amount of time to allow for departure varies greatly.  Depends on the day and time of day.  If you are returning to the states, you have to endure customs and immigration.  Passport is best for this.  Then pick up checked baggage and go to TSA.  We don't have x-ray machines on St. Croix so they must physically inspect each bag, on island time.  Now, if you are going to San Juan on Thursday morning at 6:00am, 45 minutes is plenty of time.  If it's Saturday afternoon with two American Eagle aircraft, one Cape Air, an American Jet, Delta Jet and US Airways Jet all in at the same time, two hours is cutting it close.  Too close. 

In the main (only) terminal is a gift shop, Rita's Cafe, a mail drop and an ATM.  In the departure area is a kiosk that sells drinks (soft and beer) candy, hot dogs and coffee.