Well I do want to put a plug in for micro crawlers. I love crawlers, but it's hard to find things that are a challenge for 1/10 scale for me, so I make mini's!
Okay, with that said let's move on. You could go with something in the 1/18th scale if you want to try and stay small. I have a Losi Mini Rock Crawler and love it. It is an awesome crawler that comes with good electronics and is easy to modify as it is without buy tons of aluminum hop ups (though a few don't hurt). I find that the MRC is fun around the house (in the living room, on couches, etc) and is still fun outside. You will however encounter some obstacles (if you have nice rocks around where you live) that are just too big for 1/18 scale, but 1/10 will work for it.
(If you hover over the models in this paragraph there are links to them)
So, moving on to 1/10th scale. As I'm sure you've heard by now, the
Axial AX-10 is a great crawler and almost everyone and their brother has one. Something to consider is whether you want a scale looking rig or if you want a crawler that is designed more for competitions. The AX-10 is a comp rig, but can be converted to a scale rig (as I'm doing currently). It comes as a kit with no electronics, an
ARTR (almost ready to run) and an
RTR. Oh, they just added the
RTC version too which is the "ready to crawl" version where you just need batteries, but a good crawler motor and electronics are included. The cool thing is, because of the popularity of the Scorpion, you can usually find one on craigslist in some modified form for very cheap. If you want to build a scale looking rig, Axial also makes a scale crawler called the
SCX-10. It uses the same axles as the Scorpion and currently only comes as a kit. But it is a very cool scale rig out of the box in my opinion.
The two most popular wheel sizes are 1.9 and 2.2. The AX-10 is a 2.2 competition crawler and the SCX-10 is a 1.9 scale crawler. Really what you ought to consider is, what kind of terrain to you plan to run the crawler on. If you want to compete with other people in your area (as well as have something for the kids) you would probably want a 2.2 comp style rig. If you want something smaller but still competition style, I'd say to go with the Losi MRC. If you want to build a scale looking rig then you need to decide if you want it to be based of off 1.9 size wheels or 2.2 as that will determine what kind of bodies you can use.
There are lots of other brands, models, rigs, axles, etc. but in my humble opinion I think an Axial rig is a good starting place and from there you can decide where else you may want to go (Tamiya - narrower axles, higher prices, well build, Losi - Only 2.2 rig with worm gears in the axles and front and rear independent lockers out of the box, etc.). Are there any questions you still have that I can answer?