Hi Duncan,
I’ve been into this hobby for three whole weeks, so my advice may not be the most reliable! But I did just go through the same questioning as you and I now have a little experience to tell me if I got it right or wrong.
When this question is asked on forums the 8" Dobsonian regularly seems to top the poll. They certainly offer very good bang for your buck. You wouldn't be going far wrong. However, I would still second Bill's (Tasastro) recommendations of an Altitude/Azimuth mount with a refractor telescope. They can be a good choice too.
As he says, they are very easy to set up - you simply unfold the tripod, point and look. No special setup required. Anything with an Equatorial mount will require time consuming fiddling about and re-aligning every time it's moved, and even the very simple Dobsonian mount needs to be set firmly on flat level ground and they have quite a large diameter. One of the big enemies of the amateur astronomer is any kind of wobble and vibration. It’s also likely that you might need to collimate a Dobsonian (adjust and recalibrate) which requires learning some new skills.
No matter how much you spend (within reason) you are really only likely to be looking at increasingly large clumps of white dots. You won't be seeing Cassini diving through Saturn's rings or very much in the way of fine detail on anything except the moon. An important aspect of the hobby is the reading and study required to fire up your imagination and bring those white dots to life.
A simple refractor from the Skywatcher range might be worth checking out too. Many have the added advantage that they can also be used for terrestrial viewing, so when the kids get bored with the stars they might still find other uses for it back on earth. Most astronomy telescopes invert the images - when looking at star clusters it doesn’t matter whether they’re upside down or not.
Whatever you go for will provide some successes and some relative disappointments, so don’t be too worried about getting it exactly right. Most scopes can pick up Jupiter’s moons and some version of Saturn’s rings, but they will be very small scale compared to the photos we’ve all seen. There’s always next year and your next bigger and better scope if the bug bites!
Good luck with your choice.
Cheers,
Chris