I finally have a Chicago Hardy Fig Tree, how do I baby it?

I've tried to start fig trees from cuttings but I've never succeded.
I "broke down" and bought a tiny start, less than a foot tall, in a 4" pot.
I want it to thrive and become a source for propagation.
Should I put it a larger  pot and over winter it as house plant, or  put it in the ground and insulate it with straw/hay/leaves, etc.?

Keep it as a house plant this year, be sure to water it often, because the dry winter air in the winter will dry out the soil. Next year you can plant it outside in the soil.

I usually just let them die back naturally, but some year I do bend the "canes" and lay them flat on the ground with a board/rock/etc to keep it flat, and there is no winter dieback. at which point I get two harvest.

I planted this tree in a container along side a taro.
Recently the leaves have started to die.
It has plenty of water but the edges of the leaves are kind of crunchy.
The taro  developed one very yellow leaf, which I removed.

The plants had been thriving together under ambient indoor lighting, but I've moved the fig tree to its own container which is equipped with a grow light.

Any ideas on what might be killing these plants?

William, I don't have experience with taro, but lots of experience growing figs in the north.  Make sure that your soil isn't too wet.  For winters I usually let my figs get hit by a frost to lose their leaves and then I store them in a cold dark place.  I have a room off my basement that stays 40F which is great, but I've kept them in a 50F part of my basement before.  If they start to push leaves in the late winter I would move them to light in my sunroom.  Otherwise, if they make it to spring then I move them outside for the season.  In storage I will give them a little water just to keep the soil from drying out, but I try not to overdo it.  

I also have a bunch of figs in ground.  I bend them down to the ground and pin them down with logs.  Then I cover them in dry woodchips and cover the low mound with a tarp to help keep it dry.  When the snow melts off the tarp in the early spring I pull the tarp and remove the logs and woodchips.  It's ok for them to take some 20s temps while still dormant.

I've never tried to carry a fig through the winter with leaves so I'm not sure about the problems you're having.  Too dry, too wet or too cold could be potential issues, I think.  If the leaves dropped I'd probably try to store them in a cold dark space as described above.

Oh, and for in ground, I wouldn't insulate it with anything that mice would run around under.  When I've tried leaves something has chewed off all the cambium every time.  With dry woodchips I have had no troubles.

Thanks for the replies!
I was concerned  that over watering might be an issue.
The first container is self watering , like a home made version of a self watering dog dish.
Something like this:

https://i.pinimg.com/originals/42/0b/3e/420b3e1a586fcad9d3d40ddcd1bf6e18.jpg

It was pretty happy there, until it wasn't.
The new container is a sub irrigated wicking container with lots of soil.
It's rather dried out right now, which should be good.
I'll add a little more water each day till it reaches some kind of equilibrium.

William, I forgot to reply about the pot size.  If the 4" pot has a bunch of roots that have grown out to the pot walls and are then growing along the walls, I'd definitely step it up to a larger pot.  Most plants I have gotten in 4" pots have been ready for up potting.

My poor fig trees died when I was overwintering them, I put them in a shed and they never woke back up the following year. I hope you have better luck, I'm in zone 5 so the winters are pretty tough. If you're in a cold climate find a cozy spot to over-winter your fig.

My lemon tree I brought inside in the fall and it seems to be coasting along through the winter. Not growing but not dying.