Is 2 1/2 miles enough exercise for these dog breeds?

Out of the ones you've said your interested in I think goldies, labs, boxers or a german shepherd would be good. I would lean against Dobermans and rotties as then can be a little more on the "difficult" side and you really need to make sure you socialize well with these breeds. Acd's also tend to be a bit more on the intense side. I don't know much about great dane's but I think 2 miles at a jog might be a bit much on their joints, I could be wrong so hopefully some one with some Dane experience will be able to give some advice.
I cant speak for goldies as ive never met one, but labs have plenty of energy and Boxers are going to be a bit more bouncy/lively/energetic as a breed. Oh and in terms of boxers depending on were you live you need to mindful of the heat. Honestly most healthy dogs would be happy with a two mile walk/run. If your getting a puppy keep in mind its going to be a little while before they can walk a full 2 miles. Just make sure you build up to it, especially the jogging. So in your case I think its more important to look for a breed that's personality and traits/maintnence fit in with your life style and what you want in a dog. Even a mixed breed from a shelter would be a great fit if its something your interested in (there are also breed specific rescues if you want a specific breed).

Sorry to be a buzzkill, but just adding that if you are young (I am young as well) that means you will have a certain amount of upheaval in your life. I know this isn't what you asked but it may be hard for you do find rentals, apartments, or temporary type housing with a Great Dane or a GSD. Great Dane's because they are so darn big and GSD because they are on almost every "banned" list.

I would go with a Goldie, Boxer, or Doberman (don't let it get its ear/tail cropped). I personally find labs to be incredibly unpredictable temperament wise and annoying as puppies. However, if you meet the parents and find them to be calm and friendly, I would certainly consider the lab. Goldie's and Boxers would do fine with the exercise level you describe, Dobermans as well if you do some training every day and give him lots of stimulating toys/games during down time. If you find a nice lab, you'll have the added bonus of going outside and tanning or reading while you play lazy fetch with the chuck it!

Australian Cattle Dogs are INTENSE!! They are bred to seriously work. I put them on the same level as a border collie in terms of exercise and mental stimulation needs. I almost think it is a bit unethical to have these dogs if you do not plan to work them. Unlike border collies, they have a bent for human aggression that stems from their use as cattle guards.

I get where you are coming from with being a bit lazy in terms of exercise. I aimed to get a relatively low energy dog (one that would be done for the day after a 4-5 mile run). Well, as my husky mix hit a year and a half, his energy level has blow off the roof! We run for 45 minutes a day, play off leash with friends for about an hour, and do approx 30 mins of training every day. Even that isn't enough for Bear! The only thing that gets me motivated enough to do so much work with him everyday, is the fact that he literally stands over me and licks my face until I get out of bed in the morning. If he doesn't get exercise after the morning run, he starts to steal my shoes. So good luck, I feel your pain. I always wish Bear was a coach potatoe like my puppy Loki (and me).

I would agree that if you are uncertain about future housing (young, don't own your own house, think it likely you will be looking to rent again in the course of this dogs life, especially if you aren't able to afford to pay a lot for housing), you should reconsider any breed that is commonly on banned breed lists. Am I reading it right that you have 3 other dogs already? That alone would make finding housing really difficult, I would want to avoid making it worse. Rotties, Dobermans, and GSD are usually on banned lists in housing. Boxers may be, but are much less likely. Danes will likey be hard to find housing with as well.

Also, if you already have 3 dogs, I would imagine you don't want a fourth dog that requires the bulk of your energy/attention. GSD, cattle dogs, and Dobermans are all very energetic dogs, especially the cattle dogs. To my knowledge Rotties also tend to be pretty intense/energetic.

If you get one of the protection breeds (GSD, Boxer, Rottie, Dobe) be careful of the breeder- go with a high quality dog, as I've heard of instability in certain backyard bred lines. Also, a high quality breeder will better be able to match you with a lower drive dog- it would still be a high energy dog but on the lower spectrum of the breed.

To my understanding Danes are not very high energy dogs, and border on lazy once they outgrow their puppy stages. Plus they are a breed very prone to health problems. Definitely be careful with the breeder and be fiscally equipped for medical problems.

You have 3 small dogs, right? I would be mindful of prey drive in the breeds you're looking at. Small things running (even other dogs) can often be overwhelming for high prey drive, excitable dogs, and you may be setting yourself up for a hellish puppyhood.

Personally if I were you I would look at goldens or labs. They're great additions to multidog households, are active and outdoorsey without being unbearable, and are easy to find housing with. Be weary of poorly bred dogs, though, as both have health issues; cancer is very common in both breeds.