whats a good first rifle?

You have three issues.

First - if you are shooting a rifle and your neighbors can hear it and might call the cops - then you live in a place where it is not safe to be discharging a firearm. I own several suppressors. I 'could' easily shoot things that come into my yard - nobody would hear a thing - but I do not do it because it is not safe.

Second - for coyote and fox - I have seen them hit square with a 22LR and then run a mile before dropping. Normally I recommend a 22 as a good first rifle. The ammo is cheap and this means you can shoot allot for your $$ and become a decent marksman.

Third - for coyote and fox - the 17HMR or 22 Hornet is a great choice.

Next - to get rid of fox and coyote in a urban area - you should be trapping them. Traps work 24/7 while you are asleep, at work or school. You just need to be careful and put them into places you have only seen the coyote and fox walking - this way you do not catch your neighbors dog or cat. There will be hell to pay when this happens. Snares are best. Go visit www'funketraptagsandlures.com and they sell them by half dozen. If you search some of my older posts you can get some great info on how to set them.

If you live within the city limits of a municipality, it's unlawful to discharge a firearm. And "good" and "cheap" can't be used in the same sentence for *anything*. As far as quiet, shooting anything other than .22 Shorts is going to make a racket, unless you're shooting sub-sonic ammo in a suppressed firearm (which would be illegal without the proper ATF tax stamp). And for the game you're after, head shots with a .22LR are feasible, but I seriously doubt you have sufficient skills in that area, since this is a "first rifle". And there's that pesky noise issue again.

Just get one of those toy airsoft guns.

I'd get yourself a break open .223 and I say that for 3 reasons;

1. You cant make it jam/ease of use (well you "could")

2. You'll learn to make one shot count(making you a better shooter)

and 3. They arent too expensive, roughly costins 250-400.

You cant shoot this rifle without the cops being called UNLESS you are far enough away from others, AND it is LEGAL to do so on your property.

I wouldn't particularly worry about it being quiet. If the neighbors call the cops and it is legal to fire a firearm in your back yard, maybe the police will bi***slap the neighbors and teach them some manners. The boys and I shoot quite frequently in the back yard.

Shooting a gun is some thing that is quite serious. Most states have a safety ZONE around houses to stop people like you from shooting around houses. In vest in a rifle shooting club.

For your purpose I would say 22lr. You can get a nice 22 for under 200.