Membership with recurring fee (monthly or yearly)
If you mark the payment as pending (see screenshot 1 below) then the resulting membership will be pending.  When you update the payment, the membership will be automatically updated.

To set the member status to Inactive after payment hasn't been received for three months, go to Administer menu » CiviMember » Membership Status Rules.  Click Edit next to the Grace status, and set the end event to "Membership End Date" and "End Event Adjustment" to "3 months".  This creates a three month grace period from the membership end date, and will change to "Expired" after that (assuming you haven't changed other membership status rules).