I am getting into building my first fishing rod, and I am picking out a blank. Is starting with an ice rod a good choice?

Not in my opinion.  Surprisingly, they are about the hardest rod to build, IMO, due to the very flimsy blanks.  They are so flexible that wrapping is very difficult.  Hard to control the blank even under the fairly light force of the thread under tension.  

 

You may find it different.  I find multiple piece rods the easiest since one can have either both halves, or either alone, in the wrapper, whichever suits the builder best.  Even fly rods are much easier than ice rods.  Of course, if you're wrapping a fairly stiff ice blank, my comments are invalid.

 

Another MI builder builds and sells them like crazy.  He does some really nice grip/seat combinations.  There is a lot of room for creativity in ice rods.  Lots of new developments in reels over the last 5-10 years.

 

Check out ThorneBrothers.com for reels, Jannsnetcraft.com for ice rod blanks and components.

I started with building ice rods like you're talking about doing.   I will second it's kinda a pain to learn because the blanks are so flimsy. I ended up making a custom wrapping station out of wood to help support the blanks a inch on either side of the guide it made it a little easier. I think a power wrapper with the rollers for support would work much better and make ice blanks easier to work with. 

I've built about a half dozen ice rods.  I won't build any more.  They were the hardest rods I've ever built.  The thin blanks make it very difficult to maintain proper thread tension while wrapping and guide alignment is another PITA.  Trying to tweak a guide left or right is impossible.  The blank torques and the guide doesn't move.  And finding components to fit a blank with a 1/8" OD isn't easy either.  All of my stuff is prebored at 1/4".  I had to make arbors from wood dowels so I could glue on the seats and grips.