Considering you are receiving a check from your customer, account_check_writing will be of no use for you. account_check_writing is to write a check to your supplier.

Receiving a check is like receiving cash or a wire transfer. You should have at least 1 journal per payment method; this means that you need to have a journal called "Checks" of type "Bank and Checks". In Accounting > Customer Payments, you can use the "payment ref" field as the check number. A good practice is also to scan the check and attach it to the customer payment if your bank website doesn't provide or keep forever the image of the check.

Now, you need to make a distinction between having received the check (in the mail) [1] and having deposited the check at the bank [2] and having the amout in your bank account [3].

1&2. You can use the "Draft" and "Posted" statuses of customer payments to specify the difference between [1] and [2]. Draft would mean it's received and Posted would mean it's deposited at your bank.
For 3, you will have to use bank statements.