From what you have indicated, (zoos, insects, birds and deer from your surroundings), you can divide these into probably a number of general categories: animals in captivity, animals in the wild, birds and insects. While this may be a bit of an over-generalization, a lot of the general "rules" that you have probably learned already about composition do apply - rule of thirds, leading lines, etc. Remember though, if you miss the eyes, you have missed the shot and the eyes have to be in focus. I'm sure I may get arguments about that, but unless you are collecting butt shots, this is one rule I follow. As far as the rule of thirds is concerned, it is mostly used regarding placement of the animal or bird in the frame. If you are shooting one standing still, then it is always the best to put it in such a position that it has room to move or look into the frame. In the case of birds in flight (BIFs), then they are usually placed so that they have room to "fly" into the frame.
You will need a telephoto lens. I use a Canon 100-400mm II with a 1.4 Mark III extender on it for most of my wildlife photography. You should also invest in a good tripod as it will come in handy in your zoo shots.
1) Animals in captivity - in a lot of situations, these animals will not be as active as their counterpart in the wild, so they shouldn't present too many problems. For those that are simply lying around you have to decide whether you want a full body shot or a head shot and compose accordingly. You can probably use aperture priority for most of these shots. If they are moving, then you may want to follow it with your camera set on shutter priority and a slightly faster speed depending on how fast they are moving. Most of your shots will probably be in landscape mode, but if you are shooting taller animals such as a giraffe, then portrait mode will probably work better. Portrait mode may also work better for head shots depending on the animal and how close you are to it.
2)Animals in the wild - these will be the ones you probably have to track down, regardless, they will be moving, unless you go on a safari to Africa where they tend to ignore people and their jeeps. Your guide would be able to give you guidelines on how to shoot the various animals. For Scottish deer, I can't really give you too much advice, except that this is probably something you will have to go out and track down. Maybe you can find someone who actively hunts them (assuming this is legal) and see if they have any advice for you.
3)Birds - these come in a couple of categories, those that are not moving (standing/sitting still or perched on something), those that are moving (in flight or running along a shoreline, etc.). Those that are standing still can often be shot in portrait mode using aperture priority. For those that are moving, I often shoot them in Shutter priority mode and adjust my speed and ISO accordingly. Each situation can be different - is the bird moving erratically, or is it just gently floating along on a breeze. There is an on-line guide that you might be interested in -
Secrets of Digital Bird Photography - you will find the links to following pages and a table of contents by clicking on the link at the bottom of the page. You might also want to check out Art Morris's blog. I find it informative, although you do have to remember that he is selling his products and services -
Arthur Morris/BIRDS AS ART. There are others on bird photography, but he is considered one of the best bird photographers. I know I learned a lot from attending a couple of his workshops. That is another area that will give you some "education" in wildlife photography - workshops. I subscribe to a couple of British photo mags and I always see field workshops advertised in them, so they shouldn't be too hard to find.
4)Insects - this is a completely different sort of thing than wild animals and birds, because you are really talking about macro photography. I would suggest that you Google "insect photography", You will find enough references to keep you busy for a long time. you can also watch the Macro section in TPF for postings of insects.
One of the things you might want to think about is to find one or two photographers that cover the subject, or subjects, that you are interested in and subscribe to their blogs, You will, of course, find a lot of examples on this Forum and others - it is simply a matter of finding a couple of them and seeing what people are posting. For example:
Wildlife Photography | Stephen W. Oachs
Dr. Wayne Lynch Canada's Wildlife Specialist
Mike Lane Wildlife Photography
British Wildlife | David Lloyd Wildlife Photography
The real key is just practice, practice, practice and then practice some more. Be patient with yourself and don't be afraid to experiment with your imagery. Digital is cheap, so take lots of different shots to see what sort of things work for you.
I do hope this helps, but, again, if you have further questions please post and there will be knowledgeable folks here that can answer your questions.
WesternGuy