there are many choices of lens' but heres some info on the two you have mentioned
Canon EF 75-300mm f4-5.6 USM III £236.24
good lens, will allow you to take pics from a good distance away, has a USM focusing motor (focuses faster and quieter, great for moving targets)
Canon EF 70-300mm f4-5.6 IS USM £398.99
the bigger brother of the 75-300 as it has Image stabiliser too but your paying a lot for it
Canon EF-S 55-250mm f4-5.6 IS £169.99
again a good lens, has image stabiliser which helps with camera shake and getting a good pic, it wont make a dog sit still, but at least the background wont be blured
, does not have a usm focusing motor, so its the same as your kit lens as far as focusing speed/noise goes
all the lenses have the same aperture sizes so theres nothing to choose between them there (smaller the aperture number eg 2.8 instead of 5.6, means it lets in more light and allows you to use a faster shutter speed (again helps to reduce blur) also means the depth of field is shorter, so you can blur the background softly and still have the item your focusing nice and sharp)
it all depends what you want to do with your camera, what type of pics you want to take, as there are different lenses for different jobs, you could get something like the 70-200 F2.8 IS, but thats about 1600 quid
if money is tight, the 55-250 is a good lens with good reviews, the IS is handy at the longer end of the lens (zoomed in) as it helps steady your shot, I dont think the 75-300 is worth £60 extra unless you dont need the IS, and need it to focus faster, if you have more money in your budget, let me know what you wnat to take pics of and I will see whats out there for you that fits your needs
Phil