Is it obligatory to buy a used car instead of a new one to avoid compulsory insurance, with the fear that the used car may not be suitable for needs and cause problems?

There is no harm in buying a new car with commercial insurance on it if you are compelled to do so. Commercial insurance is forbidden unless a Muslim is forced into it, in which case the sin is upon the one who coerced him. It is permissible to take out the minimum legally acceptable insurance if it is impossible to avoid it or find a permissible alternative, in accordance with the Almighty's saying: "So fear Allah as much as you are able" and His saying: "But whoever is forced, neither desiring [it] nor transgressing, there is no sin upon him."