Congratulations Phil, enjoy it!
If you're wanting to get out with your baby/toddler these are well worth the money, and good for at least a couple of years (by which time your upper body strength will be the envy of the neighbourhood). Not only for running (only when your baby is 6 months + as dougie says) but for taking on walks on rough terrain with ease. I used to borrow my neighbours (they were rare when my first daughter was born) and as dougie says, a fantastic work-out pushing all that weight, and no agonies over baby sitting. Not to mention the bonus of the baby usually going to sleep!
I got used to not moving my arms quite quickly, but you may find you have a slightly different gait as a result of leaning on the handle bars a bit.
Be careful with oncoming traffic, dogs etc and get a strap which you attach to your wrist and the handles just in case you let go on a downhill section! Excuse me for stating the obvious but your baby will need more layers of clothing, covers etc than you might think as they're not moving and are quite exposed to wind etc.
Good luck with your baby.