From the OP:
my 3 year old has seen me clean/ accustoming myself with my new gun, and has shown alot of interest. Not sure as how to properly teach her respect for them.
Kids learn a lot from watching you. You show an object great respect and great care, they will notice that.
I would avoid giving any object that a child has shown interest in the additional allure of being forbidden. Let the child know you'll show the item to them any time that she asks. (Before embarking on that, make sure your spouse agrees.) That way, there's no temptation to search out the gun on her own and "sneak a peek"--all the child need do is ask.
In short, I'd handle (and DID handle) early exposure of children to firearms the same way you'd handle their exposure to any object that posed significant danger if the child were to handle it unsupervised. How did any of us handle the issues of hot stoves, boiling water, sharp knives, household chemicals, etc. with regard to child safety?
First, you limit (as in, try to eliminate) unsupervised access. Then, you teach your kids about them, via watching you safely use them (for example, watching you use knives and the stove to cook); and then later by having the child help you: have them "chop vegetables" with you and them holding the knife; and later still with the child actually chopping the vegetables, under your direct supervision, just as you have taught her to do. With firearms, that would involve (at the right age) letting her "help" you clean the gun, and bringing her to the target range (with eye and ear protection).
Bottom line is that limiting access, by itself, is less dependable than both limiting access AND age-appropriate training. And that training is not "one and done" or as simple as having them recite a few rules: instead, you can demonstrate the rules and engage in active training EVERYTIME you handle firearms in the presence of your children.
One downside, in my experience: raising your kids to consider a firearm as just another household item (that is indeed hazardous if used improperly) means that they may come to see guns as rather ho-hum: "Want to go the range with me? You can shoot some balloons and pop them!"
"Nah. There's a new Pokémon I'm trying to catch. Maybe next time."