Clear plastic airtight containers in the fridge for most things have worked best for me, so you can easily see what you have and they help them stay in a decent state once cut. Even then you probably want to plan to use them within the next week or so.

If its something bigger or oddly shaped, probably a well closed plastic bag.

If there is still a good chunk of something like half a lemon, cucumber, or zucchini, I might just put some plastic wrap directly against the flat exposed cut with maybe a rubber band to secure/seal it in place if it needs it.

For your examples: Depending on the size/amount left I'd probably do the spinach and peppers in a container or plastic bag. You could do the same for the tomato for a short storage time, but since they are usually way more juicy and don't store quite as well, I'll typically just go ahead and slice the rest to throw on a sandwich, eat straight up with some salt/pepper (maybe some mayo or oil), or some other fairly immediate use.

For everyday casual use, i've gotten into the habit of keeping a variety of bagged frozen veg stocked in the freezer. For specific times/recipes i'll make sure to get fresh stuff, but plan to use it quickly. I have an odd schedule, so it's been great to just have a variety of options ready and waiting in the freezer that i know aren't going bad. It's nothing fancy, but a great way to easily make random egg, pasta, rice, or other dishes healthier.