If you can only buy one power saw get a circular saw.
If you can only buy two powers saws get a circular saw and a bandsaw.
If you can only buy three power saws get a circular saw and a bandsaw and miter saw (sliding preferred).
If you can only buy four power saws get a circular saw and a bandsaw and a miter saw and either a table saw or a scroll saw depending on your needs.
If you can only buy five power saws get a circular saw and a bandsaw and a miter saw and a table saw and a scroll saw.
A circular saw is extremely versatile. It is portable, and can be battery powered. There are small circular saws with 6" or less diameter blades, 8" saws are common, 10" are available. The cutting depth will be less than half the blade diameter. The blade can be angled and will have depth control. There is no limit to the width or length of a cut. A straight edge and some clamps make it almost as good as a table saw but not quite as convenient to use for straight smooth accurate cuts. Sliding track devices are available at reasonable cost to give table saw like accuracy. There is no better tool for cutting 4’x8’ sheet material except a huge incredibly expensive table saw.
A bandsaw can only make a cut as deep as its throat, 12" or less for most 2 wheels saws but much deeper for 4 wheel saws. Just about and bandsaw can cut through wood up to 6 inches thick. Band saws can cut angles and curves and can be used to carve wood to any convex shape. Band saws are excellent for ripping boards and cutting other materials like hard plastic, foam, and some can cut soft metals.
A miter saw is good for cross-cuts. Fast, accurate and easy to line up the cut. 8" to 10" saws are common, the width of a board you can cut across will be a little less than the blade diameter. A sliding miter saw can make wider cuts. Most are compound miter saws and cut be angled in two directions. If you are only doing fine carpentry it won’t be that useful if you have a table saw or band saw but if you are going to by cutting many pieces to size, like when framing a wall or siding a wall or building a deck you’ll really want one.
A scroll saw (or sabersaw or jigsaw or keyhole saw) is useful because you can cut curves and start cuts in the middle of piece by drilling a hole first (or even by gouging with the saw but I don’t recommend it). Blades can are usually mo more than 4" long or less but longer ones are available.
The can cut at angles. These saws don’t have the power of the other saws and vibrate a lot. Clean accurate cuts are difficult and they’ll move slowly through heavy stock. Cutting out shapes in the middle of a piece of wood is their most valuable feature.
A table saw is the king of power saws. The two ends of the spectrum for table saws are small benchtop or portable (contractor) saws and large cabinet saws. An 8" saw is suitable for a lot of work but may lack power for thick boards. 10" saws do quite well, 12" and larger saws are available and very expensive. The saw height can be adjusted to cut rabbets and dados (partial cuts through a piece of stock). A table saw needs a fence for ripping wood and should have a miter fence for cross cuts. A table saw’s ability to cut large pieces of wood is somewhat limited by it’s table size. Table extensions can be added but often do not stay flat with the surface of the main table. The larger the table the more useful the saw will be for larger stock. The depth of a cut will somewhat less than the diameter of the saw blade. Good portable table saws are available for under $500. A quality cabinet saw will cost at least $1000 new but good deals are available on used ones. There are some intermediate hybrid table saws that are small cabinet saws for somewhat less than $1000 last time I looked. Do not buy a used Craftsman table saw. There are a million of out there and they are usually in bad condition shaky, and have hokey belt drive systems.
Someone mentioned radial arm saws. I think they are annoying and stupid but many people have found them practical to use. They’re hardly different than a compound sliding miter saw.
If you want one tool that does everything get a ShopSmith. Except you’ll need to add the band saw and jig saw and it won’t be a very good table saw. But it is also a drill press, router, lathe, sanding disk, grinding wheel, and you can add a belt sander, joiner, planer, mortiser and other devices. They have variable speed control and a compound angled table. Great tool to have for many of those purposes, it just sucks as a table saw. They’re available used but often not in great condition, missing parts, and most available used models have an older pulley based speed changer with less power and speed range than the newer models with an electronically controlled motor. Don’t buy a used one alone, get someone who knows the product to evaluate what’s being sold.