Welcome to the forum and to bonsai. I think you should slow down a little and do some reading and research. Your plan has several questionable elements. Now that the tree is in leaf, it is not the ideal time to transplant. Unless you have a compelling reason to re-pot it I feel it would be prudent to leave it as it is until next spring.
You could do what is known as a 'slip-pot' this year. This is where the tree is moved to a slightly larger pot without disturbing the roots substantially. If you do this you will miss an opportunity to begin working the roots until it is re-potted properly.
Regular potting soil is not generally used for bonsai. Although it is counter intuitive the shallower a pot is the poorer the drainage. To counter this a very gritty, open, free draining medium is preferred. Particles about the size of the head of a matchstick are about right.
The larger pot you describe is indeed way too big and, depending upon your intentions, the smaller one may be as well. I have a Maple about the size of yours that I potted earlier this year, it is in a small flat that is 8 X 12 X 3 deep. This seems to be good fit for this tree. It allows room for root growth but is fairly shallow which helps in preparing it for its future life in a bonsai pot.
I purchased this tree in 2005 as a one year seedling and it is just now beginning to show some potential. I know it does not look much like a bonsai now but sometimes you have to allow a tree to be a tree for a while in order to grow out and gain some girth and character.
All of this assumes that you are anxious to begin training it in the near future. Another option would be to pot it up, probably in the smaller of your new pots, and simply allow it several years of growth before any type of training begins. By doing so you will end up with a better tree in the long run but it will slow down your bonsai aspirations for 3-5 years. If you choose this path I still think doing it next year is a better choice. You can then be more aggressive with the roots than if you simply slip-potted it this year.
So first decide if you feel the trunk is something you can work with or you would like it to bulk up a little more first.