If my bottom tier is a 14" round, how large should my base cake board be?
Trying to figure out if a 16" or 22" would look better?

Also, are the 1/2" thick cake boards sturdy enough for a three tier, 7", 10", 14"?

Thanks!

I like 4" larger boards, so I'd use an 18".

Yes, 1/2" thick boards or drums are sturdy enough... just make sure you use your hand underneath to support while lifting instead of lifting from the edges only.

Get a 16" board. The 1/2 cake drum is very sturdy-you will be fine.