To start with buy the best trike you can afford, the extra money will generally buy you better materials, construction and safety. Steer clear of the licensed trikes that feature images from children's TV, generally in order to pay for the license to use the characters image the manufacturer is forced to cut back on the production costs and materials.
It is important to buy a trike that fits your child correctly. Smaller front wheeled tricycles are designed for smaller children and have a low seat giving the trike a low centre of gravity when in use. This ensures it remains stable and doesn't tip over when the child corners, especially at speed, scaring your child and potentially putting them off riding for life! It's therefore important that you buy a tricycle that will fit your child now and not one they will 'grow into'. It's important that the seat is fully adjustable and secure when fixed into position and that the trike has a good stable, wide wheelbase.
Tricycle seats come in a variety of shapes and sizes, with some having a seat back for extra support, some are adjustable in two dimensions while others simply move up and down. Whatever option you go for it should be shaped to ensure your child is comfortable when riding as it's difficult enough to learn to pedal without having to do it with a sore bottom. Handlebars should have comfortable grips and the pedals should have a good non slip surface.
Many trikes come with parent handles that allow you to push your child along before they get the hang of pedaling or to allow them to rest their legs in between pedaling sessions. This handle should be removable once your child gets the hang of pedalling themselves and the trike should freewheel when the child is being pushed to prevent potential accidents. Many parent handles are height adjustable to prevent the parent from straining their backs, some trikes have a steering lock to prevent the child from crashing into obstacles and there are even some models that allow the parent to steer using the parent handle!
Generally speaking metal frame bikes are more stable as the metal frame lowers the trikes centre of gravity giving better stability when cornering.
Other things to look for are warning flags on low rider style bikes that alert car drivers to the presence of young riders they might not be able to see easily from behind the wheel. Another great accessory is a bell, not so much for safety but for fun.
Finally before your child goes riding please buy your child a cycle helmet, even small falls can be potentially serious and helmets are available at incredibly reasonable prices.
So armed with this knowledge, it's time to buy that first trike, go to the park and have FUN!