What I mean by that is, is there a way to make it so everything that appears on the canvas is hidden/invisible, and have it so my vector shapes/images only appear inside rectangle/panels?
As of now, if I am to create a comic using the pen tool, and some parts of the vector are outside the rectangles (panels) I made, I would either have to use the knife tool to cut off the vectors outside, or hide the vectors outside the panels with white rectangles (since my artboard is white).
My way of doing things is time-consuming, and just really crappy in general. Is there another way? Can I actually create panels?
One technique to use would be masks.
The basic idea is to use a rectangle with no fill (but probably a stroke) for each individual panel. Place the rectangle above the vectors/images it's intended to contain, then select the whole group and choose "Modify > Mask > Group As Mask". Then to improve the visual results, select the mask thumbnail in the Layers panel and in the Properties Inspector, choose "Path Outline" plus "Show Fill and Stroke".
Panel by panel, this should work well. The downside is, once you've masked a panel, you won't be able to easily edit its contents without ungrouping. (But you can easily ungroup and regroup, so that's not a huge deal.)
Another technique to consider would be something like your second approach, where you're hiding vectors with white rectangles. If you made a single large rectangle representing your page, and then created smaller rectangles representing each panel, you could the select them all and choose Modify > Combine Paths > Join. This would create a composite path that you could place at the very top of your Layers panel stack. It would basically mask (or cover up) the whole page in one fell swoop. The advantage here is that this would simply sit at the top of your page, and the elements beneath would be easily accessible and editable (with no ungrouping needed).
1 -Select the vectors, group them, and then cut them to the clipboard (Edit > Cut).
2 -With the rectangle selected, choose Edit > Paste Inside.
You can reposition the vector group inside the rectangle by unclicking the little link icon between the maskinng rectangle and the group. If you need to reposition the vectors in the group individually, ungroup them, which wil break that mask group, make your adjustments, and repeat tsteps 1 & 2.