Used or new is a question I struggled with for a while. I think there are a few relevant questions to help steer the decision:
1. How soon do you want/need it? From ordering until delivery, mine took 5 (!) months.
2. Do you intend on tuning it to gain more torque and mph? (This can be done by purchasing a Powerbox and helps with hills and overall comfort amongst other cars. See user @kennethnilsen69's posts for more info). All models after 6/2016 block tuning as of now. Tuning also potentially voids warranty, if the Twizy still has one.
3. How many "extras" do you want? The Bluetooth audio kit, alu wheels, and paint color are all pricey adders when buying new. Buying used, there usually isn't a huge difference in price of those with and without these extras. I personally bought new without these extras, and added them personally by finding good deals on used items.
Again, my choice was to go with new because of the warranty. My Twizy is 2 months old and now in the shop with an apparent defect motor. For me, the warranty was wise
Regarding the battery, others can speak more to that, but I have the impression that very few have needed replaced. I believe Renault estimates their lifetime at ~10 years. No one has had a Twizy for more than 5. And yes, I believe per contract, the battery must be insured.