I am not familiar with the species of tree that you have so I cant tell you specific care info. The tree in question almost looks like a birch or aspen to me but I cant be sure. If it is a birch or aspen, I am not sure how successful you will be growing it in southern California which is where I think you are (?). The other thing is that those species are outdoor trees and wont thrive inside no matter where you are.
One of the biggest parts of bonsai is figuring out what will grow and thrive in your area. Plants from the mountains up north will not survive in the desert in most cases and vice versa. Each species has a specific temperature range and seasonal fluctuation that it needs to survive. Some need cold in winter for dormancy, others cant tolerate below freezing, etc. You need to figure out these things for each species in relation to where you live and pick things that can survive where you are and what you can provide for growing area.
I dont think you have to put them in the ground considering the circumstances you described. I would put them outside except the jade tree, that can stay inside. Once you know what species they are, you can research what their typical ecology is and adjust accordingly depending on your climate. For example if the tree is tropical, you might have to bring it inside during the winter, but during the summer it should be outside in the sun, etc.
None of these are ready for a bonsai pot. We dont put trees in bonsai pots until they are pretty much fully developed trees. These need to grow, probably for many many years before they are ready for that. In fact, you might grow quite bored waiting that long. You could use some wire to put some movement into the long trunk if you want but I would not trim anything because doing that will slow down the growth.
Until we can get a definite identification on the species, it is hard to be able to give specific information.
You put your location in your profile. That is good and will help us answer your questions better.
If you are someone that is constantly moving around and unsure of what kind of growing conditions you will be able to provide, I would recommend looking into ficus bonsai trees, specifically ficus retusa or ficus microcarpa (dont buy a ficus benjamina). They can be grown indoors and in many cases can do well with supplimental light if you cant put them outside in the summer (which they prefer). Trying to grow and outdoor tree inside will most likely lead to alot of frustration for you not to mention a dead tree.