The one in the living room we call our Baby Jesus tree. Sam willingly surrendered his little "Charlie Brown Christmas tree" from last year for this purpose. It's just a little 18-inch artificial tree, but it's just right for this first year. We have hung all the ornaments we have that relate to Christ's birth on it, which isn't many... so far.
I'm keeping my eye out for good ornaments for it, and hope to get a slightly larger tree (maybe 3 or 4 feet tall) -- if the finances allow-- after Christmas when they are all marked down.
Ornaments about the first Christmas are tough to find, so I'm going to borrow my parents' idea of buying solid color balls and writing with permanent marker the names given to Jesus and what He gave us that first Christmas. (e.g. salvation, Prince of Peace, Emmanuel). Then every year, when we hang them up, we will read them and talk about them. (We haven't done this yet -- I can't decide if I want to write on the balls I already have, which are a bit large for a little tree, or buy some new littler ones for this special tree.)
Our large tree in the family room features our special family ornaments -- mementos from trips, the kids' special ornaments (baby's 1st Christmas, etc), photo ornaments (one of my favorite kinds), and the ones we bought the first year we were married. It is full of memories of our family and is very special.
On the same table as the Baby Jesus tree, we set up the Nativity scene. It's a ceramic one we were given as a wedding gift. The kids love playing with it, so I'm looking for a tougher one that can withstand their loving attention. (I'd like one with Jesus separate from the manger so we can put him in on Christmas morning.) I found a very simple one at a gift shop near us, but it was a bit more than I was prepared to spend without spousal approval!
Last year we bought an Advent book with pieces that pop out each day of December. We read the story of Jesus' birth and add a figure to the scene every night at bedtime. By the end of December last year, Sam had the whole story memorized! This year, I've put some of Luke 2 on Elli's Dynavox so she can tell parts of the story too. She really likes this, and it pleases me that she goes to public school and shares the Bible with her classmates and teachers. (They can't stop her from saying what she wants to say, after all!)
So how are you remembering Jesus' birth with your family?