Forget the '06 unless you just want to kill'em and leave 'em.

A .223, .22 BR, 22-250, 220 Swift,.243, 6mm rem for most ranges out to 400yds. 50-60 grain pills for the .224's and 58-85's for the 6mm-.243
.17HMR( 100 yds or less with head shot)
.204 for 200 or less if you shoot boiler room shots
.22WMR for under 75 yds

I like bolt guns for accuracy and are easy enough to load and shoot a follow up shot, however, the new semi auto AR's, DPM's and Bushmasters are very accurate semi's and well built. They offer a more rapid sequence of follow up shots.
Scopes should be anywhere from 3x9x40 to 6.5-20x40 or 44. You can buy a cheaper varmint rifle that will shoot well, but don't skimp on the scope. You'll appreciate the clarity and focusing ability of a better quality scope and the adage holds true" you get what you pay for". This is very true when it comes to buying glass foryour rifle.
A good set of camo, binoculars, bipod or shooting sticks and 2or 3 calls; a howler, cottontail distress and depending on where you hunt, a jackrabbit screamer or fawn distress and mouse squeeker. You can opt to purchase an electronic caller, but they are somewhat expensive.
Get a good DVD on Coyote hunting and HAVE AT IT!!!