The difference between the .22-250 and the .223rem is about 10% velocity, 20% in energy.

I used a .22-250 in high school and college for yotes and benchrest shooting, but switched over to a .223rem a few years back when I changed over to a heavy barreled AR-15. To keep things simple (haha, at least in theory), we got a .223rem bolt action for my fiancee's coyote rig.

In my experience, the only practical difference between the two is the cost. The .22-250 is often in a long action, while the .223 is in a short action. The .22-250 is a larger case, i.e. more powder = more cost. Most of my loads used magnum primers for the .22-250, while the .223 can use standard primers. Brass for the .223 is considerably cheaper than the .22-250 also. So for the volume shooters, like benchrest shooters and varminters, the .223 is much cheaper.

The power difference is essentially moot, if you hit a coyote with a .223rem, it will die, just the same as it will with a .22-250. The velocity difference makes the .22-250 a slightly flatter shooting round, but it DOESN'T mean a difference of feet vs inches. I looked up a load for both with the same 50grn bullet zeroed at 100yrds, the .223 drops 24", while the .22-250 drops 18". 6" seems like a lot, but you're already holding over 18", shooter skill and estimation accuracy will be MUCH more important than the velocity/drop difference.

The .243win is a great cartridge too. The ability to handle heavier bullets, and the higher powder capacity makes it MUCH more versatile than the other 22cal's. However, the price to play is much higher. Whether you're reloading or buying factory ammo, the .243win costs at least 50% more to shoot than the 22cals.

Personally, if you're on a tight budget so you can only afford ONE rifle and you're looking to get a versatile rifle that can pull duty as a deer rifle OR varmint rifle, offering precise bullet placement over LONG ranges, a .308win or .300WSM in a heavy barrel is the way to go.

Off your list, I'd personally get the .223rem, then get a .300wsm later for the bigger stuff. If you're limited to ONE gun, then get a .308 or .300wsm... And reload...

If you expect to shoot 400 yards with any regularity I would go with either a 22-250 or .243. I don't know how set you are on buying the Edge, but I think you can get more rifle for the money buy going with the Marlin XS7. The Edge has a very mediocre trigger and is a long action, even for the short action chamberings. I would also take a hard look at the T/C Venture for very little more money. I have one in .243. The trigger is great and accuracy is outstanding. They guarantee 1 MOA. They also have a $50 mail in rebate on the Venture right now.