I want to add custom block with custom logic to customer account. Is there any preferable inheritance in this case fro new block?
It depends on what you need.
For a simple text block
\Magento\Framework\View\Element\Template should be enough.
If you add something in the dashboard you might want to use
\Magento\Customer\Block\Account\Dashboard as a parent class. It already contains methods for retrieving the current customer, the account url, the address url.
Do not use inheritance, if it is not necessary.
Moreover, blocks are private classes of modules, this class may be modified in next versions of module.
Should not use extending
\Magento\Customer\Block\Account\Dashboard for using only one method. This class have many dependencies, which not needed in your block. Inheritance will increase coupling between objects, arguments count, stability in your class and your module will become non-reliable.
Use inheritance from
\Magento\Framework\View\Element\Template and implement only the necessary methods for you