Re: Coyote Gun
For that range either is great for yotes. Both can be had in short compact light weight rifles by multiple manufacturers. My 243win is an older ruger m77, nothing fancy about it, walnut stock, blued finish,about the only thing bad i can say about ruger is the trigger in my gun was shit...I replaced it with a timney and have never looked back. I shoot hornady 100gr sp or 95gr ballistic tips for deer and 75gr hp for yotes and about everything else. I i do my part the rifle will shoot clover leaf groups at 100yd until the barrel gets hot roughly 12-14rnds, groups open up slightly but nothing other 1 moa. I have a 3-9x40 leupold on it and can't complain about anything else, i got the gun when i was 12 for Christmas and have killed everything from crows to deer with it, excellent caliber for the range your planning to shoot. I can find ammo at almost any walmart if I'm in a pinch, 22-250 is just as available. Both calibers are easily re-loadable, relatively in-expensive and all around great calibers. If you don't have a deer rifle buy a 243win, if you plan on hunting mostly yotes get the 22-250, with the right loads it will cleanly kill deer as well. I'm not nearly as familiar with the 22-250 as i am the 243, before I start a whole world of shit I'll just say I've taken deer and coyotes with both i prefer the added knowledge that i have a little more room for error with my 243win.
As far as scopes go for the money it's hard to beat nikon for the money, i bought a predator special in 4-5-14x40 for my ar-15 build a while back and absolutely love it!!! For me it's about ideal my ar is in 223, and for right around $300 i couldn't pass it up.
If you don't have any real preference on brand i'd check out the thompson center bolt actions, haven't had a chance to try one out but if they're half the rifle t/c claims they are it's a hell of a deal. I own 1 older rem 700 and the 2 older m77 rugers and all wear timney triggers. Savage's accutrigger if adjusted right is scary close to the performance I get with my timney's and it'll save you the extra $150 i had to pay to have a trigger that wasn't shit in my rifles.