When you use Migration Assistant you have the choice of what to include. It's better not to include applications, but to install them separately. If you migrate your account it will bring over all your documents etc. belonging to the account, and also all the preferences and registrations (so that you will be able to continue using applications without having to re-register them, excepting only any where the registration is tied to the specific hardware).
There is an important point to understand. Do not create a user account with the same name on the new Mac before migrating - doing this will cause all sorts of problems. On a brand new Mac you can migrate in the initial setting up process; on one which has already been used you need to avoid this clash of accounts.
However, you imply that this is a second hand Mac on which you want to keep the previous owner's applications; strictly speaking you are not allowed to do this (other than with free ones, of course), and in the case of Apple applications they will be tied to his Apple ID and won't be updatable even if they work. With non-Apple applications transfer of ownership would be at the discretion of the manufacturer who would, if they choose, issue a new licence.