is it enough to keep precautions that we do for internet banking or is there any other things we need to consider for securing wallet
If someone gains access to your internet banking, you can easily revert all the damage they did by calling your bank.
This is not the case with crypto currencies. So a higher level of security is definitely needed.
You should not store amounts you are not willing to lose on a machine which is connected to the internet (no web wallet, mobile wallet, desktop wallet).
For higher amounts use either a hardware wallet, paper wallet or an air-gapped storage on a dedicated device.
Also, don't forget one of the most important things: Common sense.
I believe more people lose their coins trough scams and shady 'investments' than trough malware.