I was amazed at how much I use a miter saw when I finally got one. You can make a lot of the same cuts with a hand held circular saw that you can with a miter saw, but the miter is so much easier to use and a whole lot easier to be more accurate. Some cuts may be theoretically possible with a circular saw, but I would not even attempt them. If you are into fine carpentry, such as furniture making, I think a miter is essential. For rough carpentry, like building a coop, you can do it with a circular saw but I find the miter to be a real convenience.
I find a table saw to be most useful for ripping boards. I rip a lot of 2x4's. You cannot do that with a miter and it is real hard to do a good job of that with a circular saw. If you do get a table saw, get a good one. Those cheap ones are no good for ripping through the 1-1/2" thickness of a 2x4. How big a piece you can cut depends on the size of your table and guide, but most of the time I use the method below for straight cuts on plywood. I do have a good table saw, but I don't use it for much besides ripping boards.
When I want to make a straight cut with a circular saw, I make a jig using clamps. Say I want to make a straight cut the length of a piece of plywood, I take a straight board and clamp it to the plywood to run the saw along. You have to allow for the distance from the outside of the saw that is following the guide to the inside of the cutting blade. You'd think the saw manufacturers would make that easy by making that a specific whole number distance, but no, I have to measure in 1/16's of an inch.
Both the table saw and the miter saw have their uses. Which one you get if you only get one will depend on what type of construction you are going to do. In either case, I advise getting a good one. A cheap one of either will not do what you want and will cause a lot of aggravation. I think a good one is a lot safer too. I'm a whole lot more comfortable ripping a 2x4 with my good table saw than using that old cheap one I had.