In response to your questions:
Should I quit meat/dairy/eggs cold-turkey (cold-tofurkey?)? Or is it easier to "ease" my way into my new diet?
It won't really be hard to quit cold-turkey because you are not quitting a habitual practice. With that said, you could, if you wanted start with going vegan one day a week to get a taste of food prep, options, etc.
When I changed to a vegetarian, I did so for a whole week to try it. Others will try it for 30 days or so.
If you want to get an idea of how you might feel (long term) on a vegan diet, you'll want to try it for a long(er) term, like 30 days. I doubt you will feel any different from doing a vegan-Monday type of routine.
Also, if you do go vegan for any period of time, and decide it isn't for you, that's when I would "ease" BACK into a regular omnivore diet.
Am I likely to experience physical symptoms when I change my diet? Feelings of hunger? Weakness? Stomach pains? Cravings? Anything else?
Assuming that you are getting enough nutrients, which should not be a problem, you should only experience positive side effects if anything. You may, on occasion when you get very hungry, have a craving for meat or cheese or some food you have not had in a while. But, rest assured, once you start eating something, those cravings will go away. And over time, you will not crave what is not in your vegan diet.
Should I consult a doctor before/during/after the change of diet?
This is a tough call. I think in general it is a good idea to consult a doctor before dramatically changing diet or exercise routines. But, be prepared to not really be supported in your vegan efforts by most doctors. Doctor's will give advice based on medical research and their advice may be based on research that does not support vegan diets.
Are there any gotchas I need to be aware of when grocery shopping or dining out, to be sure I'm ordering things on (or at least a close as possible to) my new diet?
I think depends on your reason for going vegan. If you are just doing it for a lifestyle/nutrition change, if you get a soup made from chicken stock as opposed to vegetable stock, you probably won't know or care. But, however, if you are changing due to your beliefs against animal cruelty and the like, you may care. Soup stocks are probably the biggest gotchas as most chain restaurants use chicken stock. You can also tell your waiter that you are vegan before ordering so they may alert you to vegan options.
What do I need to take into account to ensure that I am eating a complete diet?
Unless you eat the same vegetables and meal every day, it's almost impossible not to get complete nutrition from a vegan diet. And believe me, you'll want to find different recipes as salad every day gets old very quickly.
Once I'm on my new diet, will I suffer physically if I break the diet occasionally, and eat meat/cheese/etc if that's all I have available?
This depends on each individual's body. If you go vegan for a year (for instance), and then one nice have a 24oz porterhouse steak, I think your body will definitely not like it. Trial and error and small portions is probably the best you can do.
And of course, recipes will be helpful. But again, I think this will be the easy part to answer.
There are several places to find vegan cookbooks. I definitely recommend getting (at least) one to start. You'll find there are ingredients that you may never have heard of before. It's a learning experience. Just be mindful that some (many) vegan recipes require long preparation. So maybe look for "easy vegan" or something along those lines. Many vegan recipes suggest soaking beans overnight. That is OK, but you don't need to do that. Canned beans are fine too.