I'm currently working on an HD game. My previous game was also HD.
There's not a lot you need to do differently. Previous game had views and viewports set to 720p, and all assets were made with that resolution in mind. Later, we switched up the viewports to 1080p and the game looked way smoother on 1080p displays. Eventually we supported arbitrary resolutions so the game looked smooth in any monitor. Assets were still 720p, but you can still see the benefits in jumping to higher resolutions. Smoother cameras, smoother scaling, smoother rotations, smoother movement.
If your characters are not too texture heavy (for example, if you're using skeletal animations) I'd recommend storing them in a higher resolution than you usually render them, so they still look good when increasing the resolution, or when doing zoom-in effects or whatever. At the same time, there's things you might not actually need to have at high resolutions and might still look great when upscaled, like certain particles or certain objects that are not too important.
Know what to scale down and what to scale up and you'll do well.
If it helps, my current game has 1080p assets and features hand-drawn frame-by-frame animation and I've yet to run into memory issues.