The first decision is purely personal – would you (and your husband) rather be prepared for the birth of a child with a disability or would rather not know and deal with it if and when it happens? No one else can answer this for you. Based on this decision, you can decide which tests you want to do.
There are a number of tests that are used for screening for Down Syndrome. The AFP test was originally designed to pick up neural tube defects (things like spina bifida). In that case, a protein known as alpha fetoprotein [AFP] is high. They discovered along the way that statistically if the AFP is low than the chances are greater that the fetus has Down Syndrome – they don't know why. When combined with testing for two other proteins and called the triple test, or three other proteins and called the quad test, the ability to statistically predict Down Syndrome is even better. These tests are useful for younger women to see if it is worth doing an invasive test. It is not completely accurate as it is only a statistical correlation, so we do not recommend relying on this in making any decisions. It is probably worth having the test done to look for neural tube defects.
If the test showed you were at higher risk than expected for your age, you could consider doing a test called nuchal fold thickness. This is an ultrasound that is done early during the first trimester. It has been shown that the skin of the neck on fetuses with Down is thicker than a normal fetus, which is the basis for this test. In laboratory conditions it has been shown to pick up about 85% of Down fetuses. This might help deciding whether or not to do an invasive test.
Halachically there is a debate as to whether one should do the invasive tests. One attitude is that, since one would not abort an infant with Down Syndrome, why take the risk of causing a miscarriage with an invasive test? The other attitude is that it is worth doing the test, as most of the time the fetus is ok and the mother can then be relaxed about this issue.