iv'e done quite a bit of wildlife photography in the past and most of what has allready been suggested is good advice
over time there's a couple of things iv'e learned and shutter speed isn't as important as you might think i have good sharp images at relativly low shutter speeds especialy when using a tripod or something to rest on
in order to keep the whole subject in focus i try to keep the apeture around f7/f8 and the iso below 400 this way i can attempt to keep the whole subject in focus with little as possible or no noise
it's sometimes easier to set the camera to manual and dial in the desired settings ( ie f8 , iso 200 and the shutter speed at 1/250th with camera rested or on a tripod ) and see what the exposure is like by snapping a couple off
if it looks overexposed raise the shutter speed if it looks underexposed ( a little underexposure is not a bad thing and can be easily rectified as long as the iso is low so no noise is introduced ) open the apeture a stop or raise the iso bearing in mind you don't really want to be much above 400 iso or as a last resort drop the shutter speed a little
in a perfect world settings of 1/500th or more shutter speed , F8 at 100 iso would be perfect but seldom achieved in our typical british weather
here's a couple of examples to show what i mean about shutter speed not being that important
example 1
the settings i used for this photo are
appeture at f6.3 , shutter speed at 1/500th and 200 iso
the camera used is a canon 50d and a canon 300mm F4 L prime
example 2
settings for this photo are
appeture at f6.3 , shutter speed at 1/50th and 400 iso
the same camera setup was used
as you can see both are reasonably sharp despite the difference in shutter speed
same tree same woodpecker different days different light / weather
shooting through glass is less than ideal and as allready said should really be avoided but a little post proccesing can usually get rid of the infuences that shooting through glass has on the image ( loss of contrast ) by darkening the shadows a little
a good lens for not a lot of money is one of the older 300mm F4 L primes ( non IS ) these can usually be had for around the 500 quid mark second hand
add the canon 1.4 x teleconverter and you end up with 420mm f5.6 L glass lens for less than 700 quid if you buy the converter 2nd hand
as far as lenses go that in my opinion is a bargain and an ideal entry into wildlife