My last car had a torque converter autobox. It cost a lot to repair. I asked the autobox specialist what he thought of CVTs. He said not to touch them, as they cost a fortune to repair if they go wrong. He then corrected himself and said only have one if it is under warrranty and you sell it before the warranty expires.
Of course, this raises the question of how often do they go wrong. I have no idea. They are quite common now. Toyota use them and have a 5 year warranty as standard, so if they go wrong it will cost Toyota.
I bought a Jazz CVT and paid extra for a five year warranty.
If buying second hand you can try to check when the fluid was changed. If you are not paying too much, you could see if you could get warranty or just take the risk. All second hand cars involve risk.
I do like my CVT.