There's not really lot to change in the picture output settings of a Sky+ box with HDMI out.
The only noticeable change would be altering the HD Resolution Output setting from 1080i to Automatic or 576 or 720p. When set to Auto', the box will change output resolution between 576 and 1080i to match the resolution default of the channel. IOW, HD channels are shown at 1080i, and SD channels at 576. The TV is then responsible for all scaling. You'll notice this most by how long the picture blanks out for when flicking between SD and HD channels. Setting to 1080i fixes this for a small penalty in the scaling up of SD res content.
If you've set to either 576 or 720p, then that will bork your HD quality good and proper. Make sure your Sky box is set to 1080i. Do all the onscreen confirmations to make sure that the setting sticks. Double check the menu setting before you exit the setup menus on the Sky box.
Going hand-in-hand with output resolution is the Screen Aspect Ratio.
All HD content is designed to be shown in a 16:9 format screen window. This is why fewer and fewer TVs have a button on the remote to change the picture aspect ratio. You might find though that there's still a TV menu setting to override this. The correct settings are generally either Auto or 16:9, but each has its own caveats and rely on the content being correctly formatted or correctly flagged by the broadcaster if the TV needs to adapt.
Where you can really mess up the picture is by setting the screen aspect ratio to 4:3, or even worse, Zoom. Check your settings and if in doubt stick with Auto.
The rest of your TV settings will make a smaller difference to the focus quality. The Overscan and the Noise Reduction settings should be set to OFF. Have a look at the TVs motion processing settings. When set too high the TV can make the images look like there's an oddness to the motion. It's called Soap Opera Effect (SOE).
It's worth mentioning at this point that it's common to find TVs where they have individual picture set-up memories per source signal. Some even go as far as allowing bespoke settings per signal resolution, so HDMI 2 @ 1080i can have a different setup than HDMI 2 @ 1080p, and again different for HDMI 2 @ 2160p SDR, and 2160p HDR. This means setting up for one HDMI input or the App settings (if that's an option) doesn't mean that those settings will be carried across to all other sources.
Have a play with what's been suggested so far then give us some feedback.
