JFOZ & Russdogg91...
Fellas, some friendly advice.
IF a rimfire is the only gun you have access to, or your local laws state that is all you can use, then give it a try.
But, don't expect to have a killing shot with either caliber...unless you're within 50 yds, & make a "dead-center of head" shot.
Rimfires just don't pack enough "punch", regardless of what some folks say.
If you have access to either a 12 gauge, or a centerfire rifle, do so.
JFOZ...as far as what you truly "need", (aside from the gun), a call that you are comfortable using that creates a prey distress sound, such as cottontail, or jack rabbit. (Doesn't matter if you have those critters in your area, as long as your sound is convincingly "hurt")
If you have an open-reed call, this time of year pup distress works well, as pups are dispersing, & there are still plenty of other things to eat besides rabbit.
If you're new enough to not know what pup distress is, (sounds like you might be), think "stepping on a dog's tail".
You make this sound on an open-reed by "pulling" your top lip/teeth back across the reed, towards the tip..."yip, yip, yip, yip".
Having camo is great, & should be worn head-to-toe, but not absolutely necessary to get started.
Having a soft foam pad, or something, to put under your butt is a good idea.
If you're hunting in a brushy, or heavily timbered area, binocs aren't necessary. However, if you're hunting in open areas, they are a help.
Aside from that, the best advice I can give you, is...#1) PRACTICE your calling long before stepping foot onto your hunting area; #2) Sit as still as possible, using your eyes to scan the area, with super-slow head turning; #3) Have patience. Don't expect a coyote to come bounding into sight within the first few minutes. BUT, be prepared in case one does; #4) See #1; #5) See #1, again; #6) Don't get discouraged if nothing comes in. That's why it's called "hunting".