The Invisalign system was initially created to retreat relapsed orthodontic cases. I am shocked by the number of my orthodontic patients who tell me that they were never told they had to wear retainers in order to keep their teeth straight. Somewhere in communication between doctor and patient there is a severe disconnect. What I ALWAYS tell my orthodontic patients (whether they straighten their teeth with Invisalign or conventional brackets and wires) is that they will need to wear retainers for as long AS THEY WANT STRAIGHT TEETH. The teeth that most commonly move after treatment are the lower front teeth. In fact, if an adult has lower front teeth that are straight, they either have fake teeth or they wear a retainer. To answer your specific question about the type of retention you should consider: I prefer clear retainers that look much like the Invisalign retainers. The reason I prefer them is because they retain the teeth the best. Their disadvantage is they wear out faster. Your other options are a fixed lingual wire retainer or a Hawley retainer. The fixed wire does a pretty good job keeping the lower front teeth straight but will not prevent potential relapse on back teeth. It also creates a potential hygiene problem in that you have to brush and floss around a permanent wire. This type of retainer also is not ideal for preventing teeth from rotating out of alignment. A Hawley retainer is an acrylic and wire retainer and probably the most common type. It is durable (will last longer than clear retainers) and will retain both front and back teeth. I have actually been using a "modified" Hawley retainer in my office for the past few years that does a much better job of preventing lower front teeth from rotating. I'm starting to like this retainer even more than the clear retainers because they are more durable. You will pay more initially for a Hawley retainer or a wire retainer but they won't have to be replaced as often as a clear plastic retainer. By the way, I will ALWAYS recommend a modified Hawley retainer for a patient that clinches/grinds because the clear plastic will not last very long. If a patient doesn't clinch and grind then a clear aligner will last several years. A Hawley retainer will last many years (they are usually lost before they wear out). Bottom line: wear a retainer for as long as you want straight teeth. Oh, one more MAJOR advantage to a clear plastic retainer: if you get distracted, go on vacation and forget your retainer, etc. and your teeth slightly move out of alignment...the clear plastic retainer will move them back into proper alignment whereas the Hawley retainer is much less effective in doing this.
Good luck!