Excellent questions, LlamaMama.
If you really want your progeny to continue to reproduce, you'll have to make sure a baby is on the way before you move them out. Sometimes they have kids on their own, but sometimes they don't. You can even have the baby born before they move, if you want. I think it also helps to give them the Family Oriented trait and Fertility Treatment before they go.
Getting them a job is a good idea. They'll continue to go to work after they move out, for the most part. As with everything else in the game, sometimes they will get a job on their own and sometimes they won't. But they normally keep the job once they have it. They don't usually reach level 10, though, without your help.
There are two ways to move them out of your household. If you have enough money in the family funds, you can purchase a house for them and move them to it just like a normal move, except it doesn't become your active household. The other way is to use the "Kick Out" option on the move screen. This doesn't cost you anything. The kicked out Sim(s) will take possession of an available house in the neighborhood and just move in. One thing with the Kick Out option is that they don't get to take anything in their inventories. For example, if the kicked out Sim has a car and it's in the personal inventory, that car will be moved to one of your other Sim's inventory when the first is kicked out. If the Sim moves to a purchased house, he/she gets to keep everything in personal inventory.
If this isn't any kind of a challenge game, it can be fun to decorate the target house and put in a nursery and kids' rooms. A lot of the stock houses in town don't have facilities for babies and kids. You can use Edit Town to customize any house in town for your new generations. Also, if you don't have the money to purchase a house for them, you can use the money cheat to give yourself just enough to cover the cost of the house. For example, the house you want to purchase for the grown up kids costs $65,000 and you only have $25,000. You can use testingcheatsenabled true and type "familyfunds Smith 90000" and it will give you that extra $65,000 to buy the house.
If you go the Kick Out route, be sure to follow them when they leave the homestead. Use pause often so that you can keep up with them. Otherwise, you may never know where they've moved to. Also, keep in mind that story progression will sometimes cause them to eventually move out of town. There's nothing to be done about that unless you can get them moved back into your homestead and move them out again from scratch.
