Jaxteller. From what you are asking and the price range you seem to be interested in, I would say go with the Howas 1500 in either 204 or 223. The 204 would be my first choice, with the 223 being second. Either will do you justice on coyotes and just plain fun shooting, if all you do is a few hunts or shoots a year. You choice between should also take in too consideration which loaded/factory ammo is available, at any give time, in your area.
As Rick and some others mention, the 35 Berger is the #1 bullet for coyotes, etc. but you would have to reload to use that one.
So given your choice of loaded/factory ammo, in the 204 go with any of the good 32 grain bullets, they will put any coyote down, with good shot placement ( which is always the case with any given cartridge)
In the 223, go with a good 55 grain bullet.
The 1/12 twist will do you just fine in 204 factory barrels. Now in time, if you have a gunsmith re-barrel your 204 have them use a good 1/11 twist.
In 223, I would say live with the 1/12, which is what most come in. but again if you re-barrel or can find one put a 1/9 twist on.
That is my humble opinion.. Just read, gain some information and always, no matter what, put that bullet in the proper spot and your animals will not leave the area.

Bill K

( And also, a big Welcome to the site, you will enjoy this group and can gain, and even add information to all of us.. Plus we like to see photo's of your weapons and game taken)