The bread used by Jesus and the disciples at the last supper was probably unleavened or non-fermented bread as we read in Deuteronomy 16:2-3:
And you shall offer the Passover sacrifice to the LORD your God … You shall eat no leavened bread with it.
It seems appropriate that bread used to remember the breaking of Jesus’ body should be unleavened as this would fit the types more accurately. For example, 1 Corinthians 5:7-8:
Cleanse out the old leaven that you may be a new lump, as you really are unleavened. For Christ, our Passover lamb, has been sacrificed. Let us therefore celebrate the festival, not with the old leaven, the leaven of malice and evil, but with the unleavened bread of sincerity and truth.
Having said that, we are nowhere commanded to use unleavened bread, so although I believe it is preferable, I don’t believe it can be insisted on. The main things to remember when taking the bread, is how Jesus died for us and how we have to die to serving sin, for Jesus. We also have to remember how the saints are one body with Jesus and there should be no schism in such a precious, God ordained union.