I see a few problems with your plan.
If you want to be very competitive, it will be very hard to train the same dog to excell in both obedience and agility at the same time. They actually require very different reactions and behaviours from the dog. Agility requires a dog that does not look at you while running but takes directions, the dog also must make his own decisions to take equipment some times before or without you even giving the command. Obedience dogs on the other hand must listen to you with military precision, all of their movement is very precise and controlled, and the dog must maintain eye contact during most of the time while performing. As the end behaviours are very different, it is very hard, especially for a novice to train the same dog to a competitive level in multiple sports. In fact majority of the pros will have dogs specifically for each sport.
Not having prior experience with dog training, you can certainly compete, but it is highly unlikely that you will become a serious competitor, not just because of your dog, but because of your lack of experience. Hence, I don't think serious competition should be your goal. You would have a lot to learn about the sport and training involved before being ready for serious competition. That doesn't mean you can't do it for fun, in which case you can get any dog you like, even a mutt from the shelter or rescue group. I think your bigger concern should be picking a breed that best suits your lifestyle and who's personality and learning style best matches your own. You will be much happier with your dog this way.
Regarding the time spent on training, obviously the more time you can commit to the training the end result will be much better. With dog training however, you can't really train your dog for 1 or 2h straight. Their brains will fry. It is far more effective to have many short sessions through out the day, 5-15 min max per session. Your dog will learn faster, it will retain the knowledge faster, and the training will be fun.
For agility training, there is also the equipment. There is a lot of training you can do at home for basic agility handling skills, such as shadow handling, targeting, rear body awareness exercises, shaping certain behaviours, but at some point, you will need to train with the equipment. Once you are becoming better (especially if you live in an apt and don't have your own backyard where you could set up your own equimpent) this will mean traveling to a training facility to use their equipment. That will add to the time budget, and will also cost.
Obedience for the most part is far easier to teach at home as you don't require that much equipment for it.
In both cases you will need instruction, so the cost of classes evens out.