I'm a beginner at hunting...B/F knows all about the Savages
I wasn't looking to spend that much right now....I'm still a full time student (broke all the time)
I have been there, though it was a couple of decades ago. I would recommend accuracy over speed of fire for a novice. Accuracy is what you need, generally, for coyotes. You might consider going to your local gun club and asking advise. People there are usually interested in helping young people get started. See if someone there is willing to point you toward a used rifle. A lot of people like to buy rifles, try them out, and then sell them and buy another. If you ask around, you can usually find a good deal. The best possible thing would be to have someone coach you on rifle shooting, so that you can make an informed decision.
If you knew exactly what you wanted, I'd suggest that you find one at a gun show, but you really need to know what you are doing when you are dealing with strangers.
I'd also recommend spending a little more money for a known name brand. The resale price will tend to stay the same if you need to sell it in the future. For a small framed woman, I'd recommend the .223 or .243.
The first is good for varmints, and can be used for deer in some states. The second is used for both deer and varmints everywhere. The only disadvantage is that the .243 ammunition is at least twice as expensive as the .223.
I am happy to be a resource for you (I teach firearms courses professionally) if you have any questions. I have seen people at gun shows get excellent rifles for about $200 - $250, but as I say, you need to have some expertise. I am hoping someone at the local gun club will help. When I have seen young women go to gun clubs, the response has always been extremely positive, helpful, and courteous.