I kept these for a while when I was little. They make surprisingly good pets.
Instead of misting them you can line the bottom of the tank/jar with damp paper towels -- that's what I used to do. Make sure it is not scented etc. Easier to clean as you just take the whole lot out and chuck it every couple of days. But if you live in a very hot house / climate it might evaporate too quick, so up to you really.
They are real escape artists... make sure you keep the lid on tight!
Also... make sure you get rid of the eggs in time if you don't want a million trillion babies. They are very cute but finding homes for them can be tricky (unless you want to ebay them as live food too!)
I fed mine privet mostly, with various other treats, & they did very well on that.
You can handle them but be careful... better to pick up twig & allow sticky to walk onto your hand than grab him/her. If you have to pick them up gently ease two fingers under torso between leg joints and lift very slowly -- but always better to coax them on to paper / twig etc as they tend to grip hard onto things... and then leave a leg behind
However, leg loss doesn't seem to be a major problem for them -- i suspect the weak leg joints have evolved as a way of avoiding predators? bird grabs leg, flies off with leg, sticky lives to munch another leaf? -- and as long as they don't lose multiple limbs all off the same side they tend to do okay, just sway a bit as they walk.
I used to have some toy plastic ladders which they used to mosey across to get food etc... very cute. They don't have that alarming tendency to scuttle -- fairly slow moving (until you leave the lid off, then they can get from home base to your underwear drawer in very little time at all...)
One warning -- don't let them crawl on your head. Detangling them from hair = not fun.