I wouldn't use that particular Diamondback on an Appleseed rifle. Fixed parallax at 100 yards makes it pretty hard to focus at 25.
You should look specifically for rimfire scopes, or scopes with adjustable parallax--the closer, the better. For instance, my 4.5-27x56 Razor is unbelievable--I've made hits at 1 mile with that rig, but it's practically useless on a rimfire.....at full magnification, I need to be 75-100 yards from the target in order to focus.
I would suggest reading up on parallax and how it can affect POA vs POI. You're new to scopes, and it's pretty important--if your parallax isn't adjusted properly, or you have your head out of position to the eyebox outside the parallax setting, it can make the difference between a solid hit or a clean miss....especially on small targets.
Read the specs on a scope before you buy one--make sure it either has adjustable p (down to 10-20 yards) or if it's fixed, its no further than 50.
ETA: I am a bit of an optics snob, and while I know for a fact that there are plenty of good, inexpensive options that work well in Appleseeds, I tend to gravitate towards the higher end stuff. Mostly because the majority of my shooting is bench or prone precision and I need more clarity and finer aiming points. I'm also twiddling my turrets as I move from short to long range and back so repeatable tracking is a must. If your goal is to zero at 25 and leave it there, you won't need the exposed turrets with zero stops, and repeatable tracking isn't nearly as important.
You should head over to PSA, Academy, or Sportsman's and take a look through a few different rimfire or adjustable p scopes to see which ones you like. Pretty much all the major manufacturers make something suitable.