The 220 and 22/250 are so close in performance that there is no noticable difference in the field. The only advantage I see to the 22/250 is the ammo is easier to find and more factory options are available. The 270 will work fine on coyotes but it is indeed overkill if you wish to save the pelt (this is important to me as I am not in the habit of thowing away $20+ dollars unless it is on guns, women, and food; scratch women, I forgot I'm now married.) The 25 calibers are good coyote guns but begin to have many of the same negatives as the 270, especially the 25/06. I have a 6mm which is pretty decent but the exit holes are a pain to sew back up too. I'm not familiar with the new 204, I would have reservations at this time as I am not satisfied with the results of the 17 Rem on the big coyotes I run across and feel the 223 and 222 are the lightest adequate calibers at this time for ranges out to about 200 yards or so.
The best advice I have for a beginner is to use an electonic call. A boom box will work fine though it may be a little big and unwieldy compared to the callers made for that purpose. A couple of tapes like a dying rabbit and/or jackrabbit will generally give you a decent start. Something to draw their attention away from you is good also, a stuffed animal that is somewhat life like works well. I have a toy that looks vaguely like a cross between an opossum and an ardvaark that works surprisingly well. A rabbit hide hung from a fence or branch works well also. Best success seems to come early morning from before sun up until about 9:00 AM with much less activity in the evening until dark. If you can hunt at night and, especially if lights are allowed, then the night time is great. If lights are not allowed, a full moon with snow cover is still quite bright out, enough to allow the use of scopes with thick or illuminated cross hairs or peep sights. Coyotes usually respond fairly quickly, they are the top predator in most areas so are not shy about taking a meal away from other animals. I generally call for 20 minutes or so before moving. In heavily hunted areas they may be a bit more cautious but still are mostly within this time frame.
For ammo, I prefer a hollow point bullet in most circumstances. They often don't exit and are less likely to riccochet in the event of a miss. I use several different guns when I have to shhot a coyote. A shotgun with lead #2 or BB shot is my preferred gun in populated areas unless noise is an issue. Then I use either an M-1 rifle in 30 M-1 caliber or a Marlin Camp Rifle in 9mm. The first I use a 110 gr hollow point and the second either 124 gr or 147 gr hollow points. I have a 22 WMR that I hope will work out for this same purpose as it is even quiter than the former guns. I'm trying 40 gr soft points from Remington in the hopes they will penetrate better than the hollow points from everyone else and transmit energy better than the FMJs. These guns will work out to 100 yards though are better at shotgun ranges. For longer work I use a 223 with 45 gr hollow points (often Winchester factory loads) and these are good out to 200 yards. Beyond that I'll use the 6mm with 80 gr bullets and write off the pelt value.
One last suggestion, find a place that will take the fur while still "in the round", i.e. unskinned. One generally doesn't get enough coyotes to invest in the time and equipment to properly care for the hides but one can usually get half the market price the whole dog if in decent shape. If there is no furrier close, look for a trapper who will take the hides off your hands. They may even be responsive to picking them up from you which eliminates a trip to where they may live. Good luck.
The best advice I have for a beginner is to use an electonic call. A boom box will work fine though it may be a little big and unwieldy compared to the callers made for that purpose. A couple of tapes like a dying rabbit and/or jackrabbit will generally give you a decent start. Something to draw their attention away from you is good also, a stuffed animal that is somewhat life like works well. I have a toy that looks vaguely like a cross between an opossum and an ardvaark that works surprisingly well. A rabbit hide hung from a fence or branch works well also. Best success seems to come early morning from before sun up until about 9:00 AM with much less activity in the evening until dark. If you can hunt at night and, especially if lights are allowed, then the night time is great. If lights are not allowed, a full moon with snow cover is still quite bright out, enough to allow the use of scopes with thick or illuminated cross hairs or peep sights. Coyotes usually respond fairly quickly, they are the top predator in most areas so are not shy about taking a meal away from other animals. I generally call for 20 minutes or so before moving. In heavily hunted areas they may be a bit more cautious but still are mostly within this time frame.
For ammo, I prefer a hollow point bullet in most circumstances. They often don't exit and are less likely to riccochet in the event of a miss. I use several different guns when I have to shhot a coyote. A shotgun with lead #2 or BB shot is my preferred gun in populated areas unless noise is an issue. Then I use either an M-1 rifle in 30 M-1 caliber or a Marlin Camp Rifle in 9mm. The first I use a 110 gr hollow point and the second either 124 gr or 147 gr hollow points. I have a 22 WMR that I hope will work out for this same purpose as it is even quiter than the former guns. I'm trying 40 gr soft points from Remington in the hopes they will penetrate better than the hollow points from everyone else and transmit energy better than the FMJs. These guns will work out to 100 yards though are better at shotgun ranges. For longer work I use a 223 with 45 gr hollow points (often Winchester factory loads) and these are good out to 200 yards. Beyond that I'll use the 6mm with 80 gr bullets and write off the pelt value.
One last suggestion, find a place that will take the fur while still "in the round", i.e. unskinned. One generally doesn't get enough coyotes to invest in the time and equipment to properly care for the hides but one can usually get half the market price the whole dog if in decent shape. If there is no furrier close, look for a trapper who will take the hides off your hands. They may even be responsive to picking them up from you which eliminates a trip to where they may live. Good luck.