You can use Setup Assistant or Migration Assistant to migrate just your user folder(s). Unfortunately I don't believe you can selectively transfer apps. If you are running an older version of macOS, then those apps may not be compatible with the OS on your new Mac in which case you do not want those apps transferred.
If you want even finer grain control, then you can put the old Mac into Target Disk Mode and connect it to the new Mac so the old Mac shows up as an external drive. Or you can enable File Sharing on the old Mac. Or you can use an external USB3 drive. With all of these methods you just manually locate the files you want to save and copy them over to the USB drive or to your new Mac.