Nice choices, I like that you chose trees with trunks that are over an inch in diameter. Many beginners pick up thin, young seedlings, and don't realize that to even begin training, there needs to be several years of trunk development. So you did well. Second I like that you sought out the bonsai show, and bought from bonsai dealers. Bonsai is three dimensional, and it is difficult to tell you what could be done in 3 dimensions using one dimensional linear language and 2 dimensional pictures. I would attend a few bonsai club meetings, observe, watch a few demos, and then when you feel ready to, take a bring your own tree workshop with one of the visiting teachers. While you are in California, I recommend Ted Matson or Peter Tea, I don't know the Florida teacher/artists. Ted Matson and Peter Tea are excellent instructors for any level student, from beginner to advanced. But if the opportunity does not present itself for a class, do attend a few club meetings to watch and learn. Nothing beats "learning live". Most clubs will allow guests to attend a few meetings before being required to join, so you can observe and learn without it costing a lot of money. Florida is also a "hot bed" of bonsai. You will be able to "plug in" when you get there. Some great nurseries are there, and you will get many suggestions from BNut, I personally don't know Florida well.
Third is I like that you chose species that will do well both in California's climate and in Florida's climate.
They told you right, these trees won't need to be repotted for a couple years. The pots are oversized enough that they will grow well to allow you to develop branch structure. The small display pots are for trees that have the development work finished. A smaller pot will nearly completely stop the trunk development and slow branch development to a crawl. There may be a point in time when you want to repot to change the angle the trunk leaves the media, or to position these trees a little deeper in the pots. You can explore the why later, no need to repot this year.
So first, do no harm, until you have a clear idea of what changes you want to make. I would try to keep the basic silhouette the same until you have a clear plan in mind for changes. Don't get hung up on "rules", first rule is "there are no rules", second rule is "see first rule". However, the Japanese aesthetic is a fully developed set of design guidelines, coherent from beginning to end, and as such if you don't know what to do, or how to solve a design problem, the Japanese aesthetic can provide ideas. Of course there are many who want to learn and follow the full complete Japanese Bonsai Aesthetics of Design. This is a noble goal unto itself, but not the "only way" to do bonsai. There is a "North American style" of bonsai, actually everywhere bonsai is practiced there are regional styles. So as to the advice about pruning out "crossing branches", only follow that if you, yourself feel the crossing branch is a distraction. Often they are a distraction from the image being created, but not always. Make no cuts unless you know why you are making the cuts. The why will be to improve either the current image, or to change the future image by forcing the tree to grow new or different branches to create a better image.
If you don't know why you should do something, don't. Your bonsai will benefit from this restraint. To keep the current basic shape, let branches grow out until 6 to 10 or so sets of leaves, then prune back to just one, or two or 3 leaves, tree will branch then, allow the cycle to repeat. This will develop finer branching, and may cause some back budding. If new shoots start on your trunks, you can decide whether or not to keep them. It is good to have a lot of branches to choose from before you "style" the tree. I would keep most new shoots, and follow the let them grow out, then cut back sequence.
Most pre-bonsai, and not ready for display trees are grown out for a number of years, usually at least 3, often 5, sometimes 10 years or more depending on species. When the tree is showing good vigor, many branches, and good root health, Only then is the tree "styled". Then maintained and developed for another similar period of time then it is styled again. So styling does not happen every week, or every year. Your trees are in the "in-between" phase, but could be ready for styling soon. No need to rush. I like growing new trees in my collection for a year or two before deciding what I want to do with them. Reason is as you become familiar with the tree, and its growth habits you will see different possibilities. Style it too soon, and you may cut off the best parts.
For example, your bougainvillea has some interesting possibilities, the trunk branches to 3 sub-trunks, if it were mine, I would be reducing it to one trunk, or two sub-trunks. BUT which two? Each has possibilities, but if you cut it off, you can't put it back on. So take your time, because each of the 3 sub-trunks has possibilities. Any one or maybe 2 could become the future tree. Live with it for a year to get your own feel for what you would like.
So nice finds, and welcome to crazy.
Hello all! I am new to posting here as I have been reading information on this site for about a month now. I still feel lost, but I believe I did all the possible reading I could do(without my head exploding with info) and I know I needed to acquire a tree and just start.I currently live in San Diego, but soon I will be moving to Central Florida. I read on this site that a good place to buy was at the San Diego bonsai club show they have in the spring. So I waited about 2 weeks for the show and read as much as possible thinking I could be a little prepared on what species I wanted and what is a good beginner. I showed up to the show to find the place packed with people buying trees and awesome displays. After going through all the trees for sale I found two that I really liked. I got the Chinese elm and a bougainvillea. I am attaching pictures....
it will be a nice change! I can't wait to do some more Florida fishing! I used to carry a pole everywhere I went. San Diego isn't much for fishing like FL is.....sorry everyone FL rules!! 
