Personally I think any quality boat will do, 12-14'. Otters are great, RMR, Tributaries, all will get you in fairly cheaply and will probably out live your use for them.
As far as rigging goes, get a trailer if you have space at home, then rigging is not an issue. From my experience its best to keep things moving. Spend as little time rigging as possible once the kiddo(s) are involved. It'll make mom happier as well as yourself. While it's true dad gets to rig, mom gets to deal with diapers, feeding, crying and worrying about them falling in...
I just know that once it was time to go, it was time to go!! and I was always very thankful for the trailer. We could be off the water and in the truck in about 10 minutes if need be. Always run the shuttle before or pay for one. Everyone will relax with experience.
With that said, we had both our boys on the water within their first month. Easy, short trips. We rigged a car seat to the front bench and an umbrella for mom and the kids, everyone was happy.
I know the water we floated very well and knew there were no issues - it's simply riffle-pool water where the river is rarely over waste deep and pretty slow so I was not slightly worried about flipping, or even getting wet for that matter.
I started with 12'er, went 13 pre-kids and up to 15 when the boys turned 3 and 5. If you stick with it and get into overnighters you'll need to go bigger than 13 at some point. 12 - 13 is fine for day trips but they fill up really, really fast on overnighters with kids. My youngest learned to walk on an overnighter - just some great experiences with them on the river from day 1. Go when your comfortable but don't wait for everything to be perfect - it never will.
We have some folks we used to float with that had kids the same time we did. They didn't get them out for the first two years and now it's a shit show every time they try. My boys know what to expect and look forward to every trip, its so much easier for us and I think most of it's that we started early and acclimated all of us to the process.
OK, I'll hop of the soap box...
Enjoy whatever you get. Just get something and get out there.
"If you dont do it this year, you will be one year older when you do"