It sounds like you have your accounts set up correctly.
The Income/Expense by Category report defaults to including just your Banking accounts. To customize reports, click on the gear at the top right of the report. The account selection is on the Accounts customization tab.
On the Advanced tab, there is a Transfers setting which defualts to Exclude internal. This means that transfers between accounts that are selected for the report, such as a transfer from Checking to a pay credit card account, are not included. But with this setting, transfers to and from other accounts will be included in the report. If you want to exclude transfers to and from other accounts to be excluded as well, change this setting to Exclude all.
From your description it sounds like changing the Transfers setting to Exclude all will do what you want, but if you need something different, please post back.
You can click on the floppy disk icon at the top of a report you have customized to save it. Reports are saved under Reports > My Saved Reports & Graphs, or you can access them via Reports > Reports and Graphs Center.
Unfortunately you may find some settings that are not saved as they should be.