What is the proper crucifix to have or to wear? I was told that a cross is not the same as a crucifix. I was told also that a cross represents that Jesus has risen and is proper to wear.
Some Protestants suggest that because Catholics often depict Jesus on the cross it means that they believe he has not risen. This is, of course, nonsense. Catholics are adamant about the Resurrection of Christ. That’s why it is written into the creed that we say every Sunday.
Depicting the cross bare is not an especially good symbol of the resurrection since the cross probably never stood bare. When Jesus was taken down from it, the crossbeam that his arms were nailed to was probably removed. It is doubtful that after he rose from the dead anyone bothered putting the crossbeam back up.
From a Catholic perspective there is little theological significance for items of personal jewelry whether or not the cross is bare. In a wide variety of art forms, Christians throughout the ages have depicted both Jesus on the cross and the bare cross depending not on theological considerations but on other factors, such as whether the medium they were working in could accommodate the human form easily and whether they had the artistic skill or craftsmanship to fashion a corpus.
Traditionally there has been a preference for showing the corpus when possible, as this is a more vivid reminder of the crucifixion (the crucifixion is the whole point of a cross, after all). However, this is not a theological mandate.
Bottom line: Wear whichever one you prefer. (Though know that most people will identify you as a Catholic if you wear one with a corpus.)