I have a LOT of various red/green/amber dot sights. I also have a couple of "holographic" (EoTech) sights, a;ong with a few Prismatic sights.
I've had cheaper dot sights, My most expensive red dot is an Aimpoint. Yeah, only one...of those.
NONE of my guns have cheap sights on them. I've given them away or they sit in a corner of a shelf.
Most of my red/green dot sights are made by Holosun. They are of a VERY high quality, with a reasonable cost.
When looking at buying, you not only have to look at the "visual", what it looks like), but what type battery, how long will the battery last, wiill the sight take a pounding ? From being dropped to handling a high "G" load.
And as one above notes...about the dot size. While on one hand, he comments about a1 minute dot, vs larger (he doesn't know how to use a dot sight!). MOST current, quality sights use a 2 minute dot. The EoTech does have a 1 minute dot, they are...expensive, and many/most do not understand the "holographic" reticle.
As I sort of mentioned, most of today's "quality" dot sights WILL withstand a .458 magnum rifle (which will bruise your shoulder after two shots !!). There's NO...pellet rifle that will put out the "G force" that a .458 Mag. rifle will. YES, a quality red/green dot sight doesn't care if the force is forward or backward.
You mention the Hawk dot sights. They are a higher, low, or lower high grade of sight. Their cost is very welcoming to most. I know they are rated to at least a mig high "G" force capability, and stand up to it. Again, backward / forward motion doesn't matter to a good sight. I've never used one on a firearm, but I have one on a pellet rifle.
One other thing to consider... Do you have an astigmatism ? Where your eyes have a difficult time seeing close AND far at the same time. Astigmatism and dot sights don't always go together. A higher quality dot sight, can be used if you understand the problem. Occasionally, the dot is "round", if you get lucky.
Otherwise a "prism" sight is the best way to go. These are sort of a cross between a dot sight and a scope. Most are of a high quality, and your eyesight isn't a bother.
One other thing about the "dot" sight. There is a design of "dot" that is a "chevron" (or upside down triangle). These have the "point" up. VERY easy to gain a sight picture. Bot some red/green dot sights and some prism sights have the chevron. Normally indicated by the initials "ACSS" in the title.
Hope this helps some.
Mike