I usually don't mix plants in containers, except for window boxes, but I don't use many large pots, either. The starting point for combining plants in containers has to be the same as for planting them together in the garden: compatibility of their needs for light, water, and feeding. To the extent that the basic horticultural requirements are compatible, you might go about grouping them as if you were arranging flowers.

That is, you would want a single container to have plants of different heights and leaf forms (e.g., a round-leafed plant next to a fern-leafed one), and you'd want the flower colors to be compatible if they will flower at the same time. On the other hand, and especially if you are using perennials, you might want to mix plants that flower at different times in order to extend the period through which the container always has something in flower. (This is less common with container gardening than with in-ground growing, because with containers you can move those in flower to the more prominent positions.)

I usually grow small plants like Viola tricolor (Johnny Jump-up) in window boxes so that they don't disappear among the larger plants. If window boxes are not part of your plans, you might want to put the containers holding the smallest plants on plant stands, tables, or whatever is available.

The height of a plant isn't necessarily a reason not to grow it in a container, unless the container would be top-heavy. You can stake container plants; sometimes it is best to locate the container next to the stake instead of inserting a stake into the container, but if your pots are deep enough to hold stakes or other supports, you can put them right into the containers. The size of the root system can be a limiting factor for perennials but it doesn't matter much for annuals.

I would be most concerned about the vining plants, but that's because I have very little trellis capacity. If you can work that part of it out, there is no problem (except that you can't move them once they have started to climb).

Thanks OKMoreh, good advice! I do plan on using window boxes, I purchased one this weekend. I will most likely put my Petunias in the window boxes, forgot to mention that I have petunias, sorry about that. I also have hooks for hanging baskets, so I plan on either putting some of my vines in them or putting up a trellis near the wall on my porch and getting the vines to climb.

The reason I thought the Cosmos would be too tall is that one variety I am growing can reach as high as 6' and that could create a problem on my deck, where it's on the 2nd floor, but I suppose I could put them in a container on the floor.

The reason I would like to combine flowers in containers is so I can grow more with the little space I have.

Hopefully I can think of something!

You are going to need a pretty big pot if you plan on combining 4 o'clocks with anything else. Mine grew to over 4 feet last summer, and they leaned a lot; I ended up using a peony cage to hold them up.

My cleome didn't get that tall, you could definitely combine that one with something else.

I would definitely use a trellis for the vines; morning glory and moon flower do not trail well... they tend to wrap around each other trying to climb up again, and get pretty tangled, in my experience. Haven't grown the other vines you mentioned, tho I am trying them this year, also on a trellis.

If your nasturtiums are the trailing kind, they would be good in your baskets.